`f(x) = (2x + 7)/(x^2 + 4)` Use the Product Rule or the Quotient Rule to find the derivative of the function.

Textbook Question

Chapter 2, Review - Problem 34 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to evaluate the derivative of the given function and since the function is a quotient of two polynomials, then you must use the quotient rule, such that:

`f'(x) = ((2x+7)'(x^2+4) - (2x+7)(x^2+4)')/((x^2+4)^2)`

`f'(x) = (2(x^2+4) - (2x+7)(2x))/((x^2+4)^2)`

`f'(x) = (2x^2 + 8 - 4x^2 - 14x)/((x^2+4)^2)`

Combining like terms yields:

`f'(x) = (-2x^2 - 14x + 8)/((x^2+4)^2)`

Hence, evaluating the derivative of the function, using the product rule, yields `f'(x) = (-2x^2 - 14x + 8)/((x^2+4)^2).`

We’ve answered 319,627 questions. We can answer yours, too.

Ask a question