Question

If $f\left(x\right)=lo{g}_{x^2}{x}^3$, write the vaue of $f^{\prime }\left(x\right)$.

Answer 1

Given

$f\left(x\right)=lo{g}_{x^2}{x}^3$

$=\frac{log{x}^3}{log{x}^2}$

$=\frac{3logx}{2logx}=\frac{3}{2}$

$f^{\prime }\left(x\right)=0$