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!!!
$\displaystyle \ln y = \ln x \ln x = (\ln x)^2$
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 $\displaystyle y = x^{\ln x}$.