Need help differentiating a function

*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?

HallsofIvy

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

*tahayassen*

Quote by HallsofIvy

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

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

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tahayassen	Need help differentiating a function Tweet 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?

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	You aren't using the product rule. You have multiplied x by the derivative of [itex](10- x^2)^{1/2}[/itex], effectively treating that first "x" as though it were a constant. It is not.