Two ways to take a derivative in python python coding shorts

sure! in python, there are multiple ways to compute derivatives. here, i will present two common methods: using the `sympy` library for symbolic differentiation and using `numpy` for numerical differentiation.

### method 1: symbolic differentiation with sympy

`sympy` is a python library for symbolic mathematics. it allows you to perform algebraic operations on mathematical expressions.

#### installation

first, ensure you have `sympy` installed. you can install it via pip:

#### example code

here’s how you can compute the derivative of a function symbolically:

### output:

### method 2: numerical differentiation with numpy

`numpy` can be used for numerical differentiation, which is useful when you have data points or a function that is not easily differentiable symbolically.

#### installation

if you don't have `numpy` installed, you can install it with:

#### example code

here’s how to compute the derivative using finite differences:

### output:

### summary

1. **symbolic differentiation**: use `sympy` for exact derivatives when you have mathematical expressions.
2. **numerical differentiation**: use `numpy` for approximating derivatives based on function evaluations, which is useful in cases where you have discrete data or complex functions.

each method has its use case, and you can choose based on your requirements!

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