The chain rule is a fundamental rule in calculus that allows us to find the derivative of a composite function.

You don’t see it at the very beginning of taking derivatives, but technically it’s still there. It’s just that the chain rule gives you multiplication by one by when it’s dx/dx.

A composite function is a function that is made up of two or more simpler functions.

The chain rule states that if we have a composite function, such as f(g(x)), the derivative of the composite function with respect to x is equal to the derivative of the outer function (f(x)) evaluated at the inner function (g(x)), multiplied by the derivative of the inner function (g(x)) with respect to x. Mathematically, it can be written as:

(d/dx)[f(g(x))] = f'(g(x)) * (d/dx)[g(x)]

It can also be written using Leibniz notation:

(df/dx) = (df/dg) * (dg/dx)

The chain rule is fairly straightforward but is also one step that some students forget at times!

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