Solution assignment 29 Product and Quotient rule

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Assignment 29

Differentiate:

$y=1-\cos^2(x)$

Solution

We can apply the product rule because we can write:

$y=1-\cos(x)\cos(x)$

We know that:

$[\cos(x)]'=-\sin(x)$

and thus the product rule yields:

$y'=0-[-\sin(x)\cos(x)+\cos(x)\cdot-\sin(x)]=2\sin(x)\cos(x)$

If you are familiar with the chain rule you can get the same result a lot easier and faster.

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