1. ## d(x^e^x)/dy'',??

Ive never been shown the technique for this differential. Anybody know it?? thnx! diff: $y=x^e^x$ hmm latex won't let me write this one, basicall y=x to the power exp(x)

2. Originally Posted by oxrigby
Ive never been shown the technique for this differential. Anybody know it?? thnx! diff: $y=x^e^x$ hmm latex won't let me write this one, basicall y=x to the power exp(x)
If you are asking what $\frac{d}{dx}\bigg[x^{e^x}\bigg]$ equals then I can help you. first note that

$x^{e^x}=e^{\ln\left(x^{e^x}\right)}=e^{e^x\ln(x)}$

So now knowing that $\frac{d}{dx}\bigg[e^{u(x)}\bigg]=u'(x)e^{u(x)}$

And that $\frac{d}{dx}\bigg[e^x\ln(x)\bigg]=e^x\ln(x)+\frac{e^x}{x}$

We can see that

$\frac{d}{dx}\bigg[e^{e^x\ln(x)}\bigg]=\left(e^x\ln(x)+\frac{e^x}{x}\right)e^{e^x\ln(x)} =\left(e^x\ln(x)+\frac{e^x}{x}\right)x^{e^x}$