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

Textbook Question

Chapter 2, 2.4 - Problem 27 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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GivenĀ `y=x/sqrt(x^2+1)`

Rewrite the function asĀ `y=x(x^2+1)^(-1/2)`

Find the derivative using the Product Rule and Chain Rule.

`y'=x[(-1/2)(x^2+1)^(-3/2)]+(x^2+1)^(-1/2)(1)`

`y'=(x^2+1)^(-3/2)[(-1/2)x+(x^2+1)]`

`y'=(x^2+1)^(-3/2)[-x/2+(2x^2)/2+2/2]`

` ` `y'=(2x^2-x+2)/[2(x^2+1)^(3/2)]`

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

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