- #1

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## Homework Statement

What is the derivative of ##f(x)=\frac {2x^2} {cos x}##?

## Homework Equations

## The Attempt at a Solution

##F(x)=\frac {2x^2} {cos x}##

So...

##f(x)=2x^2## and ##f'(x)=4x##

##g(x)=cosx## and ##g'(x)=-sinx##

If I plug these into the quotient rule I thought that I would get the correct answer.

##F'(x)=\frac {f'(x)g(x)-f(x)g'(x)} {(g(x))^2}##

##=\frac {4x cosx -2x^2 (-sinx)} {cos^2x}##

The answer i'm given is supposed to be ##=\frac {4x cosx +2x^2 sinx} {cos^2x}##.

What is happening to make ##-2x^2## positive and ##-sinx## positive?