`G(x) = sqrt(1 - x^2) arccos(x)` Find the derivative of the function. Simplify where possible.

Textbook Question

Chapter 3, 3.5 - Problem 53 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`d/(dt) cos^-1(t)=(-1)/sqrt(1-t^2)`

`G(x)=sqrt(1-x^2)cos^-1(x)`

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

`G'(x)=sqrt(1-x^2)*(-1/sqrt(1-x^2)) + cos^-1(x) *(1/2)(1-x^2)^(-1/2)(-2x)`

`G'(x)=-1+(-xcos^-1(x))/sqrt(1-x^2)`

`G'(x)=-1-(xcos^-1(x))/sqrt(1-x^2)`

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