`y = (x^2 + 2)^2 (x^4 + 4)^4` Use logarithmic differentiation to find the derivative of the function.

Textbook Question

Chapter 3, 3.6 - Problem 39 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

1 Answer | Add Yours

mathace's profile pic

mathace | (Level 3) Assistant Educator

Posted on

Given: `y=(x^2+2)^2(x^4+4)^4`      Take the logarithm of both sides of the equation, then rewrite the expression using the laws of logarithms. ``



Take the derivate of both sides of the equation. 



Substitute in for y using the given. 


The derivative is: `(4x)(x^2+2)(x^4+4)^4+(16x^3)(x^2+2)^2(x^4+4)^3`


We’ve answered 319,645 questions. We can answer yours, too.

Ask a question