`f(x) = sqrt(x^2 - 4x + 2)` Find the derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 14 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

mathace's profile pic

mathace | (Level 3) Assistant Educator

Posted on

GivenĀ `f(x)=sqrt(x^2-4x+2)`

Rewrite the function asĀ `f(x)=(x^2-4x+2)^(1/2)`

Find the derivative using the Chain Rule.

`f'(x)=(1/2)(x^2-4x+2)^(-1/2)(2x-4)`

`f'(x)=(1/2)(2(x-2))/(x^2-4x+2)^(1/2)`

`f'(x)=(x-2)/(x^2-4x+2)^(1/2)`

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

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question