Question

Differentiate the following functions w.r.t. x . log(ax)^x.

Answer 1

log (ax)^x = x.log(ax)

d. w. r. to x

\(\frac{d}{dx}\) x log(ax)

 = \(x\frac{d}{dx}log(ax)+log(ax).\frac{d}{dx}x\)

 = \(x.\frac1{ax}.\frac{d}{dx}(ax)+log(ax).1\) 

 = \(\frac1a.a.1 + log(ax)\) 

 = 1 + log(ax)