Question

Differentiate w.r.t. $x$:

$y=e^x+{10}^x+x^x$

Answer 1

$y=e^x+{10}^x+x^x$

Consider $z=x^x$

Taking log on both sides

$\log z=x\log x$

Differentiating w.r.t. x, we get,

$\frac{1}{z}\frac{dz}{dx}=1+\log x$

$\frac{dz}{dx}=x^x(1+\log x)$

Thus, $\frac{dy}{dx}=e^x+{10}^{x}ln10+x^x(1+\log x)$