`y = ((x^2 + 1)/(x^2 - 1))^3` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 21 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

1 Answer | Add Yours

gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

using the quotient rule for derivatives, 

`d/dx f(x)/g(x) = (f'(x)g(x)-g'(x)f(x))/(g(x))^2`

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

`= [(x^2-1)^3 * 3(x^2+1)^2 * 2x - (x^2+1)^3 * 3(x^2-1)^2* 2x]/(x^2-1)^6`

`=[6x(x^2-1)^3(x^2+1)^2 - 6x(x^2+1)^3(x^2-1)^2]/(x^2-1)^6 = (-12x*(x^2+1)^2)/(x^2-1)^4`

Hope this helps.

We’ve answered 318,944 questions. We can answer yours, too.

Ask a question