Question

How do you use the chain rule to differentiate `y=sin^2x/cosx`?

Answer 1

You must apply the chain rule to differentiate numerator of fraction because it's a composed function. See below how to do it...

Explanation:

`y' = (sin^2 x / cos x)^{'} = {(sin^2 x)' cdot cos x - sin^2 x cdot (cos x)'}/{(cos x)^2} rArr`

`rArr y' = {2 sin x cdot (sin x)' cdot cos x - sin^2 x cdot (- sin x)}/{cos^2 x} rArr`

`rArr y' = {2 sin x cos^2 x + sin^3 x}/{cos^2 x} = sin x + sin x/cos^2 x`