# Math Help - What Is Derivative of (f²(x))?

1. ## What Is Derivative of (f²(x))?

What Is Derivative of (f²(x))? I am confused with that square sign thrown in there.

2. Originally Posted by r2d2
I am confused with that square sign thrown in there.
$\frac{d}{dx}f^2(x) = \frac{d}{dx}(f(x)\cdot f(x)) = f(x)\cdot \frac{d}{dx}(f(x)) + \frac{d}{dx}(f(x))\cdot f(x) = 2f(x)f'(x)$

3. So then would the second derivative be:

d/dx f'(x)(f(x)*2= [2 d/dx f''(x)f(x) +f'(x)f'(x)] = 2f''(x)f(x) + 2f'(x)f'(x)

would that be right, pulling the 2 out in front?

4. Originally Posted by r2d2
So then would the second derivative be:

d/dx f'(x)(f(x)*2= [2 d/dx f''(x)f(x) +f'(x)f'(x)] = 2f''(x)f(x) + 2f'(x)f'(x)

would that be right, pulling the 2 out in front?
Yes, that is correct.

5. Great, Just want to make sure. Thanks again, defunkt