`F(theta) = arcsin(sqrt(sin(theta)))` Find the derivative of the function. Simplify where possible.

Textbook Question

Chapter 3, 3.5 - Problem 56 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`d/(dx)sin^-1(x)=1/sqrt(1-x^2)`

`F(theta)=sin^-1(sqrt(sin(theta)))`

`F'(theta)=(1/sqrt(1-sintheta)) * d/(d theta)sqrt(sintheta)`

`F'(theta)=(1/sqrt(1-sintheta)) *(1/2)(sintheta)^(-1/2) costheta`

`F'(theta)=costheta/((2sqrt(sintheta)sqrt(1-sintheta)))`

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