Question

Differentiate $x^{x^2}$ w.r.t. $x$

Answer 1

$y=x^{x^2}$

taking log both sides

$\log y=\log x^{x^2}$

$\log y=x^2\log x$

differentiating with respect to x

$\frac{1}{y}\frac{dy}{dx}=2x\log x+\frac{x^2}{x}$

$\frac{1}{y}\frac{dy}{dx}=2x\log x+x$

$\frac{dy}{dx}=y(x+2x\log x)$

$\frac{dy}{dx}=x^{x^2}(x+2x\log x)$