Question

find dy/dx for y=x^(e^x)

Answer 1

CHAIN RULE CHAIN RULE

Answer 2

\[\frac{d}{dx}x^{e^{x}}\]

Answer 3

Ok, I don't know how to make it bigger... :(
Also, Chain Rule?

Answer 4

\[\rm {dy \over dx}(f(g(x)) = g'(x) f'(g(x))\]

Answer 5

I think logarithmic is more appropriate here.

Answer 6

\[y=x^{e^{x}} \rightarrow \ln y = \ln x^{e^{x}}\]
Perhaps this makes things clearer?

Answer 7

Oh well:
\[\ln y = e^{x}lnx\]
differentiating both sides
\[\frac{1}{y}\frac{dy}{dx}=\frac{e^x}{x}+e^{x}lnx\]
\[\frac{dy}{dx}=y \left( \frac{e^{x}}{x}+e^{x}lnx \right)\]
\[\frac{dy}{dx}=x^{e^{x}}\left( \frac{e^{x}}{x}+e^{x}lnx \right)\]
done...