{"id":1016971,"date":"2024-12-27T12:21:14","date_gmt":"2024-12-27T04:21:14","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1016971.html"},"modified":"2024-12-27T12:21:21","modified_gmt":"2024-12-27T04:21:21","slug":"python%e5%a6%82%e4%bd%95%e6%b1%82%e5%87%bd%e6%95%b0%e5%af%bc%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1016971.html","title":{"rendered":"python\u5982\u4f55\u6c42\u51fd\u6570\u5bfc\u6570"},"content":{"rendered":"

\"python\u5982\u4f55\u6c42\u51fd\u6570\u5bfc\u6570\"<\/p>\n

\u4f7f\u7528Python\u6c42\u51fd\u6570\u5bfc\u6570\u7684\u4e3b\u8981\u65b9\u6cd5\u5305\u62ec\uff1a\u4f7f\u7528SymPy\u5e93\u8fdb\u884c\u7b26\u53f7\u8ba1\u7b97\u3001\u4f7f\u7528NumPy\u548cSciPy\u8fdb\u884c\u6570\u503c\u8ba1\u7b97\u3001\u5229\u7528\u81ea\u52a8\u5fae\u5206\u5de5\u5177\u5982Autograd\u6216JAX\u3002\u8fd9\u4e9b\u65b9\u6cd5\u5404\u6709\u4f18\u52a3\uff0cSymPy\u9002\u5408\u7b26\u53f7\u8ba1\u7b97\u3001NumPy\u548cSciPy\u9002\u5408\u6570\u503c\u8ba1\u7b97\u3001\u81ea\u52a8\u5fae\u5206\u5de5\u5177\u5219\u517c\u5177\u7075\u6d3b\u6027\u548c\u6548\u7387\u3002<\/strong>\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u6bcf\u79cd\u65b9\u6cd5\u7684\u4f7f\u7528\u53ca\u5176\u4f18\u7f3a\u70b9\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u4f7f\u7528SYMPY\u8fdb\u884c\u7b26\u53f7\u5bfc\u6570\u8ba1\u7b97<\/p>\n<\/p>\n

SymPy\u662fPython\u7684\u4e00\u4e2a\u5f3a\u5927\u7684\u7b26\u53f7\u6570\u5b66\u5e93\uff0c\u9002\u7528\u4e8e\u7b26\u53f7\u5bfc\u6570\u8ba1\u7b97\u3002\u5b83\u53ef\u4ee5\u5904\u7406\u4ee3\u6570\u65b9\u7a0b\u3001\u5fae\u79ef\u5206\u3001\u77e9\u9635\u8fd0\u7b97\u7b49\u3002<\/p>\n<\/p>\n

    \n
  1. \u5b89\u88c5\u548c\u57fa\u672c\u4f7f\u7528<\/li>\n<\/ol>\n

    \u9996\u5148\uff0c\u4f60\u9700\u8981\u5b89\u88c5SymPy\u5e93\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\uff1a<\/p>\n<\/p>\n

    pip install sympy<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    \u5b89\u88c5\u5b8c\u6210\u540e\uff0c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u4ee3\u7801\u8fdb\u884c\u57fa\u672c\u5bfc\u6570\u8ba1\u7b97\uff1a<\/p>\n<\/p>\n
    from sympy import symbols, diff<\/p>\n
    x = symbols('x')<\/p>\n
    f = x2 + 3*x + 5<\/p>\n
    f_prime = diff(f, x)<\/p>\n
    print(f_prime)<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    \u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u5e76\u4f7f\u7528diff<\/code>\u51fd\u6570\u8ba1\u7b97\u5176\u5bfc\u6570\u3002symbols<\/code>\u51fd\u6570\u7528\u4e8e\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u3002<\/p>\n<\/p>\n
      \n
    1. \u591a\u53d8\u91cf\u51fd\u6570\u7684\u5bfc\u6570<\/li>\n<\/ol>\n
      SymPy\u4e5f\u652f\u6301\u591a\u53d8\u91cf\u51fd\u6570\u7684\u5bfc\u6570\u8ba1\u7b97\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff1a<\/p>\n<\/p>\n
      from sympy import symbols, diff<\/p>\n
      x, y = symbols('x y')<\/p>\n
      f = x<strong>2 + y<\/strong>2 + 3*x*y<\/p>\n
      f_prime_x = diff(f, x)<\/p>\n
      f_prime_y = diff(f, y)<\/p>\n
      print(f_prime_x)<\/p>\n
      print(f_prime_y)<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5bf9\u51fd\u6570(f(x, y) = x^2 + y^2 + 3xy)\u5206\u522b\u5bf9x\u548cy\u6c42\u504f\u5bfc\u6570\u3002<\/p>\n<\/p>\n
        \n
      1. \u9ad8\u9636\u5bfc\u6570<\/li>\n<\/ol>\n
        SymPy\u8fd8\u53ef\u4ee5\u8ba1\u7b97\u9ad8\u9636\u5bfc\u6570\uff0c\u53ea\u9700\u5728diff<\/code>\u51fd\u6570\u4e2d\u6307\u5b9a\u6c42\u5bfc\u6b21\u6570\uff1a<\/p>\n<\/p>\n
        from sympy import symbols, diff<\/p>\n
        x = symbols('x')<\/p>\n
        f = x5<\/p>\n
        f_second_derivative = diff(f, x, 2)<\/p>\n
        print(f_second_derivative)<\/p>\n
        <\/code><\/pre>\n<\/p>\n
        \u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u51fd\u6570(f(x) = x^5)\u7684\u4e8c\u9636\u5bfc\u6570\u3002<\/p>\n<\/p>\n
        \u4e8c\u3001\u4f7f\u7528NUMPY\u548cSCIPY\u8fdb\u884c\u6570\u503c\u5bfc\u6570\u8ba1\u7b97<\/p>\n<\/p>\n
        \u5bf9\u4e8e\u590d\u6742\u7684\u51fd\u6570\uff0c\u7279\u522b\u662f\u90a3\u4e9b\u6ca1\u6709\u663e\u5f0f\u89e3\u6790\u8868\u8fbe\u5f0f\u7684\u51fd\u6570\uff0c\u6570\u503c\u5bfc\u6570\u8ba1\u7b97\u53ef\u80fd\u662f\u66f4\u5b9e\u9645\u7684\u9009\u62e9\u3002<\/p>\n<\/p>\n
          \n
        1. \u4f7f\u7528NumPy\u8ba1\u7b97\u6570\u503c\u5bfc\u6570<\/li>\n<\/ol>\n
          NumPy\u672c\u8eab\u4e0d\u76f4\u63a5\u63d0\u4f9b\u5bfc\u6570\u8ba1\u7b97\u529f\u80fd\uff0c\u4f46\u53ef\u4ee5\u901a\u8fc7\u6709\u9650\u5dee\u5206\u7684\u65b9\u6cd5\u8fdb\u884c\u6570\u503c\u8fd1\u4f3c\u3002<\/p>\n<\/p>\n
          import numpy as np<\/p>\n
          def f(x):<\/p>\n
              return x2 + 3*x + 5<\/p>\n
          def numerical_derivative(f, x, h=1e-5):<\/p>\n
              return (f(x + h) - f(x - h)) \/ (2 * h)<\/p>\n
          x = 1.0<\/p>\n
          print(numerical_derivative(f, x))<\/p>\n
          <\/code><\/pre>\n<\/p>\n
          \u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u4e00\u4e2a\u51fd\u6570numerical_derivative<\/code>\uff0c\u4f7f\u7528\u4e2d\u5fc3\u5dee\u5206\u6cd5\u8ba1\u7b97\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/p>\n<\/p>\n
            \n
          1. \u4f7f\u7528SciPy\u8fdb\u884c\u6570\u503c\u5bfc\u6570\u8ba1\u7b97<\/li>\n<\/ol>\n
            SciPy\u63d0\u4f9b\u4e86\u4e00\u4e2aderivative<\/code>\u51fd\u6570\u7528\u4e8e\u6570\u503c\u5bfc\u6570\u8ba1\u7b97\uff1a<\/p>\n<\/p>\n
            from scipy.misc import derivative<\/p>\n
            def f(x):<\/p>\n
                return x2 + 3*x + 5<\/p>\n
            x = 1.0<\/p>\n
            print(derivative(f, x, dx=1e-6))<\/p>\n
            <\/code><\/pre>\n<\/p>\n
            scipy.misc.derivative<\/code>\u51fd\u6570\u901a\u8fc7\u6709\u9650\u5dee\u5206\u6cd5\u8ba1\u7b97\u5bfc\u6570\u3002dx<\/code>\u53c2\u6570\u7528\u4e8e\u63a7\u5236\u5dee\u5206\u95f4\u9694\u3002<\/p>\n<\/p>\n
            \u4e09\u3001\u4f7f\u7528\u81ea\u52a8\u5fae\u5206\u5de5\u5177<\/p>\n<\/p>\n
            \u81ea\u52a8\u5fae\u5206\u5de5\u5177\u5982Autograd\u548cJAX\u53ef\u4ee5\u9ad8\u6548\u5730\u8ba1\u7b97\u590d\u6742\u51fd\u6570\u7684\u5bfc\u6570\uff0c\u7279\u522b\u9002\u7528\u4e8e\u9700\u8981\u591a\u6b21\u8ba1\u7b97\u7684\u573a\u666f\uff0c\u5982\u673a\u5668\u5b66\u4e60<\/a>\u3002<\/p>\n<\/p>\n
              \n
            1. \u4f7f\u7528Autograd\u8fdb\u884c\u5bfc\u6570\u8ba1\u7b97<\/li>\n<\/ol>\n
              Autograd\u662f\u4e00\u4e2a\u81ea\u52a8\u5fae\u5206\u5e93\uff0c\u80fd\u591f\u901a\u8fc7\u8ffd\u8e2a\u8ba1\u7b97\u56fe\u6765\u8ba1\u7b97\u5bfc\u6570\u3002<\/p>\n<\/p>\n
              import autograd.numpy as np<\/p>\n
              from autograd import grad<\/p>\n
              def f(x):<\/p>\n
                  return np.sin(x) + np.cos(x2)<\/p>\n
              f_prime = grad(f)<\/p>\n
              x = 1.0<\/p>\n
              print(f_prime(x))<\/p>\n
              <\/code><\/pre>\n<\/p>\n
              Autograd\u4e0eNumPy\u517c\u5bb9\uff0c\u53ef\u4ee5\u5904\u7406\u6807\u91cf\u548c\u5411\u91cf\u51fd\u6570\u3002<\/p>\n<\/p>\n
                \n
              1. \u4f7f\u7528JAX\u8fdb\u884c\u5bfc\u6570\u8ba1\u7b97<\/li>\n<\/ol>\n
                JAX\u662fGoogle\u5f00\u53d1\u7684\u4e00\u4e2a\u9ad8\u6027\u80fd\u81ea\u52a8\u5fae\u5206\u5e93\uff0c\u7279\u522b\u9002\u7528\u4e8e\u6df1\u5ea6\u5b66\u4e60\u3002<\/p>\n<\/p>\n
                import jax.numpy as jnp<\/p>\n
                from jax import grad<\/p>\n
                def f(x):<\/p>\n
                    return jnp.sin(x) + jnp.cos(x2)<\/p>\n
                f_prime = grad(f)<\/p>\n
                x = 1.0<\/p>\n
                print(f_prime(x))<\/p>\n
                <\/code><\/pre>\n<\/p>\n
                JAX\u63d0\u4f9b\u4e86\u66f4\u9ad8\u7684\u6027\u80fd\uff0c\u5c24\u5176\u662f\u5728GPU\u548cTPU\u4e0a\u3002<\/p>\n<\/p>\n
                \u56db\u3001\u5bfc\u6570\u8ba1\u7b97\u7684\u5e94\u7528\u5b9e\u4f8b<\/p>\n<\/p>\n
                \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5bfc\u6570\u8ba1\u7b97\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u5982\u4f18\u5316\u95ee\u9898\u3001\u673a\u5668\u5b66\u4e60\u6a21\u578b\u7684\u68af\u5ea6\u8ba1\u7b97\u7b49\u3002\u4e0b\u9762\u7b80\u8981\u4ecb\u7ecd\u51e0\u4e2a\u5e94\u7528\u5b9e\u4f8b\uff1a<\/p>\n<\/p>\n
                  \n
                1. \u4f18\u5316\u95ee\u9898\u4e2d\u7684\u5bfc\u6570<\/li>\n<\/ol>\n
                  \u5728\u4f18\u5316\u95ee\u9898\u4e2d\uff0c\u5bfc\u6570\u7528\u4e8e\u786e\u5b9a\u51fd\u6570\u7684\u6781\u503c\u70b9\u3002\u901a\u8fc7\u6c42\u89e3\u5bfc\u6570\u4e3a\u96f6\u7684\u65b9\u7a0b\uff0c\u53ef\u4ee5\u627e\u5230\u51fd\u6570\u7684\u6700\u5c0f\u503c\u6216\u6700\u5927\u503c\u3002<\/p>\n<\/p>\n
                  from sympy import symbols, diff, solve<\/p>\n
                  x = symbols('x')<\/p>\n
                  f = x<strong>3 - 3*x<\/strong>2 + 4<\/p>\n
                  f_prime = diff(f, x)<\/p>\n
                  critical_points = solve(f_prime, x)<\/p>\n
                  print(critical_points)<\/p>\n
                  <\/code><\/pre>\n<\/p>\n
                  \u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528SymPy\u8ba1\u7b97\u51fd\u6570\u7684\u4e34\u754c\u70b9\u3002<\/p>\n<\/p>\n
                    \n
                  1. \u673a\u5668\u5b66\u4e60\u4e2d\u7684\u68af\u5ea6\u8ba1\u7b97<\/li>\n<\/ol>\n
                    \u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u68af\u5ea6\u7528\u4e8e\u66f4\u65b0\u6a21\u578b\u53c2\u6570\uff0c\u4ee5\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\u3002<\/p>\n<\/p>\n
                    import autograd.numpy as np<\/p>\n
                    from autograd import grad<\/p>\n
                    def loss_function(w):<\/p>\n
                        return np.sum((w - 1)2)<\/p>\n
                    grad_loss = grad(loss_function)<\/p>\n
                    w = np.array([2.0, 3.0])<\/p>\n
                    print(grad_loss(w))<\/p>\n
                    <\/code><\/pre>\n<\/p>\n
                    \u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Autograd\u8ba1\u7b97\u635f\u5931\u51fd\u6570\u7684\u68af\u5ea6\u3002<\/p>\n<\/p>\n
                      \n
                    1. \u79d1\u5b66\u8ba1\u7b97\u4e2d\u7684\u5bfc\u6570<\/li>\n<\/ol>\n
                      \u5bfc\u6570\u5728\u79d1\u5b66\u8ba1\u7b97\u4e2d\u7528\u4e8e\u5206\u6790\u548c\u6a21\u62df\u7269\u7406\u73b0\u8c61\uff0c\u5982\u6d41\u4f53\u52a8\u529b\u5b66\u4e2d\u7684\u901f\u5ea6\u548c\u52a0\u901f\u5ea6\u8ba1\u7b97\u3002<\/p>\n<\/p>\n
                      import numpy as np<\/p>\n
                      from scipy.misc import derivative<\/p>\n
                      def velocity(t):<\/p>\n
                          return 3*t2 + 2*t + 1<\/p>\n
                      t = 1.0<\/p>\n
                      acceleration = derivative(velocity, t, dx=1e-6)<\/p>\n
                      print(acceleration)<\/p>\n
                      <\/code><\/pre>\n<\/p>\n
                      \u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u4e86\u4e00\u4e2a\u7b80\u5355\u8fd0\u52a8\u6a21\u578b\u7684\u52a0\u901f\u5ea6\u3002<\/p>\n<\/p>\n
                      \u4e94\u3001\u5bfc\u6570\u8ba1\u7b97\u7684\u6ce8\u610f\u4e8b\u9879<\/p>\n<\/p>\n
                      \u5728\u8fdb\u884c\u5bfc\u6570\u8ba1\u7b97\u65f6\uff0c\u9700\u8981\u6ce8\u610f\u4ee5\u4e0b\u51e0\u70b9\uff1a<\/p>\n<\/p>\n
                        \n
                      1. \n
                        \u6570\u503c\u7a33\u5b9a\u6027<\/strong>\uff1a\u5728\u6570\u503c\u8ba1\u7b97\u4e2d\uff0c\u9009\u62e9\u5408\u9002\u7684\u5dee\u5206\u6b65\u957f\uff08\u5982dx<\/code>\uff09\u4ee5\u5e73\u8861\u7cbe\u5ea6\u548c\u7a33\u5b9a\u6027\u3002<\/p>\n<\/p>\n<\/li>\n
                      2. \n
                        \u8ba1\u7b97\u6548\u7387<\/strong>\uff1a\u5bf9\u4e8e\u590d\u6742\u51fd\u6570\uff0c\u9009\u62e9\u5408\u9002\u7684\u8ba1\u7b97\u65b9\u6cd5\uff08\u5982\u7b26\u53f7\u8ba1\u7b97\u6216\u81ea\u52a8\u5fae\u5206\uff09\u4ee5\u63d0\u9ad8\u6548\u7387\u3002<\/p>\n<\/p>\n<\/li>\n
                      3. \n
                        \u51fd\u6570\u7684\u53ef\u5fae\u6027<\/strong>\uff1a\u786e\u4fdd\u51fd\u6570\u5728\u8ba1\u7b97\u5bfc\u6570\u7684\u70b9\u4e0a\u662f\u53ef\u5fae\u7684\uff0c\u5426\u5219\u53ef\u80fd\u4f1a\u5bfc\u81f4\u9519\u8bef\u7ed3\u679c\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n
                        \u901a\u8fc7\u672c\u6587\u7684\u4ecb\u7ecd\uff0c\u5e0c\u671b\u8bfb\u8005\u80fd\u591f\u638c\u63e1Python\u4e2d\u4e0d\u540c\u5de5\u5177\u548c\u65b9\u6cd5\u7684\u5bfc\u6570\u8ba1\u7b97\uff0c\u5e76\u80fd\u591f\u5728\u5b9e\u9645\u95ee\u9898\u4e2d\u7075\u6d3b\u5e94\u7528\u3002\u65e0\u8bba\u662f\u7b26\u53f7\u8ba1\u7b97\u3001\u6570\u503c\u8ba1\u7b97\u8fd8\u662f\u81ea\u52a8\u5fae\u5206\uff0c\u9009\u62e9\u5408\u9002\u7684\u5de5\u5177\u548c\u65b9\u6cd5\u662f\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u548c\u7cbe\u5ea6\u7684\u5173\u952e\u3002<\/p>\n<\/p>\n
                        \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
                         \u5982\u4f55\u5728Python\u4e2d\u8ba1\u7b97\u51fd\u6570\u7684\u5bfc\u6570\uff1f<\/strong>
                        \u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528SymPy\u5e93\u6765\u8ba1\u7b97\u51fd\u6570\u7684\u5bfc\u6570\u3002SymPy\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u7b26\u53f7\u6570\u5b66\u5e93\uff0c\u652f\u6301\u7b26\u53f7\u8ba1\u7b97\u548c\u4ee3\u6570\u8fd0\u7b97\u3002\u9996\u5148\u9700\u8981\u5b89\u88c5SymPy\u5e93\uff0c\u53ef\u4ee5\u4f7f\u7528\u547d\u4ee4pip install sympy<\/code>\u3002\u63a5\u7740\uff0c\u53ef\u4ee5\u901a\u8fc7\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u548c\u4f7f\u7528diff<\/code>\u51fd\u6570\u6765\u8ba1\u7b97\u5bfc\u6570\u3002\u4f8b\u5982\uff1a<\/p>\n
                        import sympy as sp\n\nx = sp.symbols('x')\nf = x**2 + 3*x + 5\nderivative = sp.diff(f, x)\nprint(derivative)\n<\/code><\/pre>\n
                        Python\u4e2d\u6709\u54ea\u4e9b\u5e93\u53ef\u4ee5\u7528\u4e8e\u6c42\u5bfc\u6570\uff1f<\/strong>
                        \u9664\u4e86SymPy\uff0cPython\u8fd8\u6709\u5176\u4ed6\u5e93\u53ef\u4ee5\u7528\u4e8e\u6c42\u5bfc\u6570\u3002\u4f8b\u5982\uff0cNumPy\u548cSciPy\u5e93\u63d0\u4f9b\u4e86\u4e00\u4e9b\u6570\u503c\u65b9\u6cd5\u6765\u8fd1\u4f3c\u6c42\u5bfc\u3002\u901a\u8fc7\u4f7f\u7528numpy.gradient<\/code>\u51fd\u6570\uff0c\u53ef\u4ee5\u8ba1\u7b97\u6570\u7ec4\u7684\u5bfc\u6570\u3002\u6b64\u5916\uff0cTensorFlow\u548cPyTorch\u7b49\u6df1\u5ea6\u5b66\u4e60\u6846\u67b6\u4e5f\u652f\u6301\u81ea\u52a8\u5fae\u5206\uff0c\u9002\u5408\u5904\u7406\u590d\u6742\u7684\u51fd\u6570\u548c\u6a21\u578b\u3002<\/p>\n
                        \u5982\u4f55\u4f7f\u7528\u6570\u503c\u65b9\u6cd5\u5728Python\u4e2d\u8fd1\u4f3c\u5bfc\u6570\uff1f<\/strong>
                        \u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u5dee\u5206\u6cd5\u8fd1\u4f3c\u8ba1\u7b97\u5bfc\u6570\u3002\u901a\u8fc7\u5728\u51fd\u6570\u503c\u4e4b\u95f4\u6c42\u5dee\u5e76\u9664\u4ee5\u5c0f\u7684\u589e\u91cf\uff0c\u53ef\u4ee5\u5f97\u5230\u5bfc\u6570\u7684\u8fd1\u4f3c\u503c\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u5b9a\u4e49\u4e00\u4e2a\u51fd\u6570\u5e76\u4f7f\u7528\u5c0f\u7684\u6b65\u957f\u6765\u8ba1\u7b97\u5bfc\u6570\uff1a<\/p>\n
                        def f(x):\n    return x**2 + 3*x + 5\n\ndef numerical_derivative(f, x, h=1e-5):\n    return (f(x + h) - f(x - h)) \/ (2 * h)\n\nx = 2\napprox_derivative = numerical_derivative(f, x)\nprint(approx_derivative)\n<\/code><\/pre>\n
                        \u901a\u8fc7\u8fd9\u4e9b\u65b9\u6cd5\uff0c\u7528\u6237\u53ef\u4ee5\u7075\u6d3b\u5730\u5728Python\u4e2d\u8ba1\u7b97\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u4f7f\u7528Python\u6c42\u51fd\u6570\u5bfc\u6570\u7684\u4e3b\u8981\u65b9\u6cd5\u5305\u62ec\uff1a\u4f7f\u7528SymPy\u5e93\u8fdb\u884c\u7b26\u53f7\u8ba1\u7b97\u3001\u4f7f\u7528NumPy\u548cSciPy\u8fdb\u884c\u6570\u503c\u8ba1\u7b97 […]","protected":false},"author":3,"featured_media":1016988,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1016971"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1016971"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1016971\/revisions"}],"predecessor-version":[{"id":1016990,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1016971\/revisions\/1016990"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1016988"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1016971"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1016971"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1016971"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}