# Simplifying this derivative...

Tags:
1. Jun 27, 2017

### Jess Karakov

1. The problem statement, all variables and given/known data
Evaluate the derivative of the following function:
f(w)= cos(sin^(-1)2w)
2. Relevant equations
Chain Rule

3. 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?

2. Jun 27, 2017

### Dick

Because they are inverse functions. $\sin(\sin^{-1}(x))=x$.

3. Jun 27, 2017

### Jess Karakov

Ah okay. I wasn't aware of this. Thank you.