# derivative question.

• Feb 19th 2010, 10:28 AM
Evan.Kimia
derivative question.
if f in sqrt(f(x)) is differentiable, would it equal to

f'(x)
------
2sqrt[f(x)] ?
• Feb 19th 2010, 10:29 AM
Evan.Kimia
trying this out with x^3, i get 2(x^3)-1*(3x^2), and i think this would yield....

3x^2
------
2(x^3)

I know this is a dumb simplification problem but i just wanted some clarification. thanks.
• Feb 19th 2010, 10:33 AM
e^(i*pi)
Quote:

Originally Posted by Evan.Kimia
if f in sqrt(f(x)) is differentiable, would it equal to

f'(x)
------
2sqrt[f(x)] ?

Let $\displaystyle y = \sqrt{f(x)}$

$\displaystyle y^2 = f(x)$

$\displaystyle 2y\frac{dy}{dx} = f'(x)$

$\displaystyle \frac{dy}{dx} = \frac{f'(x)}{2y} = \frac{f'(x)}{2\sqrt{f(x)}}$

I get the same answer as you but I'm not 100% confident it's right
• Feb 19th 2010, 12:26 PM
ebaines
Quote:

Originally Posted by Evan.Kimia
trying this out with x^3, i get 2(x^3)-1*(3x^2), and i think this would yield....

3x^2
------
2(x^3)

I know this is a dumb simplification problem but i just wanted some clarification. thanks.

Not quite right. You should have:

$\displaystyle f(x) = \sqrt {x^3}$
$\displaystyle f'(x) = \frac {3x^2} {2 \sqrt{x^3}} = \frac 3 2 \sqrt x$

An easier way is to realize that
$\displaystyle \sqrt {x^3} = x^{3/2}$

So you get right to:
$\displaystyle f'(x) = \frac 3 2 x^{1/2} = \frac 3 2 \sqrt x$