Need help differentiating a function

1. Apr 30, 2012

tahayassen

1. The problem statement, all variables and given/known data

f(x) = 2x * (10-x^2)^(1/2)

Determine f'(x).

2. The attempt at a solution

f'(x) = 2x*(1/2) * (10-x^2)^(-1/2) * (-2x)
= x * (-2x) * (10-x^2)^(-1/2)
= -2x^2 * (10-x^2)^(-1/2)

What am I doing wrong?

2. Apr 30, 2012

HallsofIvy

Staff Emeritus
You aren't using the product rule. You have multiplied x by the derivative of $(10- x^2)^{1/2}$, effectively treating that first "x" as though it were a constant. It is not.

3. Apr 30, 2012

tahayassen

Doh! I'm such an idiot! Thanks for the quick response!