Understanding Chain Rule

Thu, 28 May 2026 13:45:57 +0000

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What is Chain Rule?

The chain rules nothing but a differntiation of a function with another function.

For example:
Taking displacement, velocity, acceleration as an example

s(t)→v(t)→a(t)

Where:

displacement depends on time
velocity depends on displacement changing over time
acceleration depends on velocity changing over time ### Displacement

Velocity

Acceleration

Each graph is the derivative of the previous one.

Why chain rule is used?

The chain rule is used in Machine Learning during Backpropagation, which is the process of training the network by adjusting its weights and biases to minimize errors.

If you have two functions, f(x) and g(x), and you want to find the derivative of their composition f(g(x)), the chain rule states:

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Understanding Chain Rule

What is Chain Rule?

Velocity

Acceleration

Why chain rule is used?