# Simplifying this derivative...

## Homework Statement

Evaluate the derivative of the following function:
f(w)= cos(sin^(-1)2w)

Chain Rule

## The Attempt at a Solution

I did just as the chain rule says where
F'(w)= -[2sin(sin^(-1)2w)]/[sqrt(1-4w^(2))

but the book gave the answer as F'(w)=(-4w)/sqrt(1-4w^(2))

and I'm wondering if there is some kind of simplification I'm missing. Why would sin and sin^(-1) disappear?

## Answers and Replies

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Dick
Homework Helper

## Homework Statement

Evaluate the derivative of the following function:
f(w)= cos(sin^(-1)2w)

## Homework Equations

Chain Rule
View attachment 206165

## The Attempt at a Solution

I did just as the chain rule says where
F'(w)= -[2sin(sin^(-1)2w)]/[sqrt(1-4w^(2))

but the book gave the answer as F'(w)=(-4w)/sqrt(1-4w^(2))

and I'm wondering if there is some kind of simplification I'm missing. Why would sin and sin^(-1) disappear?
Because they are inverse functions. ##\sin(\sin^{-1}(x))=x##.

Jess Karakov
Because they are inverse functions. ##\sin(\sin^{-1}(x))=x##.
Ah okay. I wasn't aware of this. Thank you.