Three interactive solutions are given: use of the prime, the operator $\frac{d}{\mathrm{dx}}$, and the Context Panel.

In $g\left(x\right)\={\log }_a\left(u\left(x\right)\right)$, the "outer" function is ${\log }_a$, while the "inner" function is $u\left(x\right)\={\log }_b\left(x\right)$. By the Chain rule, the derivative of $g\left(x\right)$ is

 $g\prime \left(x\right)\=\frac{u\prime \left(x\right)}{u\left(x\right) \ln \left(a\right)}\=\frac{\frac{1}{x \ln \left(b\right)}}{u\left(x\right) \ln \left(a\right)}\=\frac{\frac{1}{x \ln \left(b\right)}}{{\log }_b\left(x\right) \ln \left(a\right)}$ 

Now, Maple immediately converts ${\log }_b\left(x\right)$ to $\frac{\ln \left(x\right)}{\ln \left(b\right)}$, so the derivative becomes

$g\prime \left(x\right)\=\frac{\frac{1}{x \ln \left(b\right)}}{\frac{\ln \left(x\right)}{\ln \left(b\right)} \ln \left(a\right)}\=\frac{1}{x \ln \left(x\right) \ln \left(a\right)}$ 

If $g\left(x\right)$ is entered into the  tutor using the notation log[a](x) for ${\log }_a\left(x\right)$, Maple will immediately render the problem as $\frac{\ln \left(\frac{\ln \left(x\right)}{\ln \left(b\right)}\right)}{\ln \left(a\right)}$.