Question

find dy/dx if, y=5^(x+log x)​

Answer 1

$y = 5 {}^{x + logx}$

$apply \: log \: both \: sides$

$logy \: = (x + logx)log5$

$apply \: differentiation$

$\frac{1}{y} \frac{dy}{dx} = log5(1 + \frac{1}{x} )$

$\frac{dy}{dx} = 5 {}^{x + logx} \: log5(1 + \frac{1}{x} )$