`y = cos^-1(sin^-1(t))` Find the derivative of the function. Simplify where possible.

Textbook Question

Chapter 3, 3.5 - Problem 58 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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

using above

`y=cos^-1(sin^-1(t))`

`y'=(-1)/sqrt(1-(sin^-1(t))^2) * d/(dt) sin^-1(t)`

`y'=(-1)/sqrt(1-(sin^-1(t))^2) * (1/sqrt(1-t^2))`

`y'=(-1)/(sqrt(1-t^2)sqrt(1-(sin^-1(t))^2))`

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