Solution assignment 15 Product and Quotient rule

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Assignment 15

Differentiate:

$y=\sin(2x)$

Solution

This function is not in the list of standard functions (it is with argument $x$ , but it is not with argument $2x$ ) and at first sight we do not recognize a product. Yet, by applying the double angle formula we can write:

$y=\sin(2x)=2\sin(x)\cos(x)$

and thus we can apply the product rule:

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

Again the double angle formula is applied.

If you are familiar with the chain rule you will notice that this is a faster method.

Return to Assignments Product and Quotient rule

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Solution assignment 15 Product and Quotient rule

Assignment 15

Solution

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