chain rule
Chain Rule Calculate the updated weight value using Chain rule The chain rule is a fundamental concept in calculus and plays an essential role in training neural networks using backpropagation. Chain Rule in Calculus: In simple terms, the chain rule provides us a technique to differentiate composite functions. Suppose we have two functions y = g ( u ) and u = f ( x ) . The composite function is y = g ( f ( x ) ) . The derivative of y with respect to x is found as: d y/d x = d y/d u × du/d x That is, you can find the rate of change of the outer function with respect to the inner function and multiply it by the rate of change of the inner function with respect to the independent variable. Visual Explanation: Imagine you're driving your car on a hilly road. You can think of the road's curve as a function. Now, the speed at which you're driving represents a second function, representing how your speed changes as you drive along the curve. Now, you want to know how your speed will change (acceleration) when you reach a particular steep part of the hill. For this, you'd first find out how much steeper that part is compared to the rest of the hill (the slope or derivative of the hill's curve). Next, you'd determine how your speed changes in response to this steepness.