Simplifying this derivative....

[Jess Karakov]

Homework Statement

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

Homework Equations

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?

 

[Dick]

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.