What is the chain rule?
The chain rule is a fundamental concept in calculus that allows us to find the derivative of composite functions. It states that if we have a function, y=f(g(x)), where g is a function of x and f is a function of g, then the derivative of y with respect to x is given by:
[Tex]\frac{dy}{dx} = \frac{df}{dg} \cdot \frac{dg}{dx} [/Tex]
This means that to find the derivative of a composite function, we first find the derivative of the outer function with respect to its input (treating the inner function as a variable), then multiply it by the derivative of the inner function with respect to its input.
Chain Rule Derivative in Machine Learning
In machine learning, understanding the chain rule and its application in computing derivatives is essential. The chain rule allows us to find the derivative of composite functions, which frequently arise in machine learning models due to their layered architecture. These models often involve multiple nested functions, and the chain rule helps us compute gradients efficiently for optimization algorithms like gradient descent.