`y = sin^-1 (2x + 1)` Find the derivative of the function. Simplify where possible.

Textbook Question

Chapter 3, 3.5 - Problem 51 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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

`y'=1/(sqrt(1-(2x+1)^2))*d/(dx) (2x+1)`

`y'=2/sqrt(1-(4x^2+1+4x))`

`y'=2/sqrt(1-4x^2-1-4x)`

`y'=2/sqrt(-4x^2-4x)`

`y'=2/sqrt(4(-x^2-x))`

`y'=2/(2(sqrt(-x(x+1))))`

`y'=1/sqrt(-x(x+1))`

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