Answer to Question #4004 in Differential Equations for tanmay

Question

differentiate W.R.T x :
e rest to xlogx means e^xlogx (xlogx in power of e)

please explain with steps

Answer 1

<img src="/cgi-bin/mimetex.cgi?\left (e^{x \log x} \right )' = (x \log x)' e^{x \log x} = (x* 1/x + \log x)e^{x \log x} = (1 + \log x)e^{x \log x}" title="\left (e^{x \log x} \right )' = (x \log x)' e^{x \log x} = (x* 1/x + \log x)e^{x \log x} = (1 + \log x)e^{x \log x}">