This post is a quick recap on some fundamentals of calculating derivatives, useful for image processing and deep learning.
Calculating the derivative
Given x to the power of n, where n ≠ 0.
This is known as the power rule. For example:
Derivative of a sum of functions
The derivative of a sum of functions is the sum of the derivatives:
So simply compute the derivatives one at a time then sum them individually.
Derivative of a product of functions
The derivative of a product of functions is defined:
This is known as the product rule.
Derivative of composed functions
For function composition the derivative is:
This is known as the chain rule.
If stuck, play with this calculator.