Simplifying this derivative...

  • #1

Homework Statement


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

Homework Equations


Chain Rule
eq0008M.gif


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

  • #2
Dick
Science Advisor
Homework Helper
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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##.
 
  • Like
Likes Jess Karakov
  • #3
Because they are inverse functions. ##\sin(\sin^{-1}(x))=x##.
Ah okay. I wasn't aware of this. Thank you.
 

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