Question

Derivada ?
$y = a^{lnx}$

Answer 1

$f(x)=a^{\ln x}\\a^{\ln x}=e^{\ln a^{\ln x}}=e^{\ln x\cdot \ln a}\\u=\ln x\cdot \ln a\\\\\displaystyle \frac{df}{dx}=\frac{d}{du}e^{u}\cdot \frac{d}{dx}u=e^{u}\cdot\frac{\ln a}{x}=\frac{e^{u}\ln a}{x}=\frac{e^{\ln x\cdot \ln a}\cdot \ln a}{x}=\frac{a^{\ln x}\cdot \ln a}{x}$