# Math Help - Question x^x

1. ## Question x^x

If $
\frac{{df}}{{dx}}=x^x
$
for x>0, and $
g(x)=f(x^2)$
then $
\frac{{dg}}{{dx}} =
$
?

2. Originally Posted by chaddy
If $
\frac{{df}}{{dx}}=x^x
$
for x>0, and $
g(x)=f(x^2)$
then $
\frac{{dg}}{{dx}} =
$
?
by the chain rule: $\frac {dg}{dx} = f'(x^2) \cdot 2x$

now continue

3. Okay, so $
\frac {dg}{dx} = f'(x^2) \cdot 2x
$
which means that $
\frac {dg}{dx} = x^{2x^2} \cdot 2x
$

Thus $
\frac {dg}{dx} = 2x^{2x^2+1}
$

Correct?

4. Originally Posted by chaddy
Okay, so $
\frac {dg}{dx} = f'(x^2) \cdot 2x
$
which means that $
\frac {dg}{dx} = x^{2x^2} \cdot 2x
$

Thus $
\frac {dg}{dx} = 2x^{2x^2+1}
$

Correct?
yup