`y = r/sqrt(r^2 + 1)` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 27 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`y=r/sqrt(r^2+1)`

`y'=r*(-1/2)(r^2+1)^((-1/2)-1) (2r) + 1/sqrt(r^2+1)`

`y'=-r^2(r^2+1)^(-3/2) + 1/sqrt(r^2+1)`

`y'= -r^2/(r^2+1)^(3/2) +1/sqrt(r^2+1)`

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

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

`y'=(1)/((r^2+1)(sqrt(r^2+1)))` 

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