Suppose I have a function def f(x): return torch.sin(x) I can find the derivative of the function at a point as folllows: x = torch.tensor([2.], requires_grad=True) y = f(x) y.backward(retain_graph=True) x.grad However, this requires computing the value of f(x) in order to find it’s derivative, ... More on discuss.pytorch.org

How To Take Derivatives In Python: 3 Different Types of Scenarios In this video I show how to properly take derivatives in python in 3 different types of scenarios. The first scenario is when you have an explicit form for your function, such as f(x)=x2 or f(x)=ex sin(x). In such a scenario, the sympy library can be used to take first, second, up to nth derivatives of a function. This comes in handy for complicated functions, but can later on be EXTREMELY useful for computing Lagrange's equations of motion given strange trajectories. The second scenario is when you collect data and want to compute a derivative. In such a scenario, the data is often noisey, and taking a simple derivative will fail since it will amplify the high-frequency component of the data. In such a case, one needs to smooth data before taking a derivative. The ideal library for managing this is numpy. The third scenario involves functions of an irregular form. By this, I mean that your function can't be written down as simply as "sin(x)" or "ex". For example. f(x) = "solve an ode using some complex odesolver with parameter abserr=x and compute the integral of the answer". In this case, derivatives can't be computed symbolically, but one can use scipy's derivative method to get a good estimate of df/dx at certain values of x. More on reddit.com

I see SICP, I upvote. Cheers! More on reddit.com

As some people have said, doing approximate derivatives numerically is pretty simple. To expand, you can make a higher order function that takes in a function and returns the function's approximate derivative as follows: def make_derivative(func,h): def derivative(x): return (func(x+h) - func(x))/h return derivative This returns a function that behaves like a derivative, and of course the smaller your h, the better your approximation. This is nice because you don't have to enter the function you are differentiating every time you compute a value of a given derivative. For example: def square(x): return x*x d_square = make_derivative(square,.0000001) >>>d_square(1) 2.0000001010878066 >>>d_square(2) 4.000000091153311 More on reddit.com