Hi, I just spent a while doing math homework and I am really stuck on this last question. It reads find the first derivative of

y = x^ln(x)

can someone please help me so i can move on.. Thanks!!!

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- Oct 9th 2008, 03:25 PMCucc1137first derivative with natural log
Hi, I just spent a while doing math homework and I am really stuck on this last question. It reads find the first derivative of

y = x^ln(x)

can someone please help me so i can move on.. Thanks!!! - Oct 9th 2008, 03:27 PMJhevon
- Oct 9th 2008, 03:29 PMmr fantastic
$\displaystyle \ln y = \ln x \ln x = (\ln x)^2$

Differentiate both sides with respect to x (use implicit differentiation on the left hand side):

$\displaystyle \frac{1}{y} \frac{dy}{dx} = 2 \, (\ln x) \, \left( \frac{1}{x}\right)$.

Now make $\displaystyle \frac{dy}{dx}$ the subject and substitute $\displaystyle y = x^{\ln x}$. - Oct 9th 2008, 03:30 PMCucc1137
is that last step the derivative or do you take the derivative of that part?

- Oct 9th 2008, 03:33 PMmr fantastic
- Oct 9th 2008, 03:34 PMCucc1137
so is it

dy/dx = (2)(lnx)(1/x)(x^lnx)

can u simplify that down alot of just the basic (2lnx/x)(x^lnx) ??? - Oct 9th 2008, 03:37 PMmr fantastic
- Oct 9th 2008, 03:38 PMCucc1137
so what i have at the end is right .. or can you simplify more??

- Oct 9th 2008, 03:40 PMmr fantastic
- Oct 9th 2008, 03:43 PMCucc1137
o alright.. thank you