If the function $f(x)={\mathrm{log}}_{2x}{x}^{2}$ is given, what is ${f}^{\prime}(4)$?

I tried to use the formula for derivative of logarithm but here the base is 2x, so it made me confused.

Note that the answer is $1/(18\mathrm{ln}2)$

I tried to use the formula for derivative of logarithm but here the base is 2x, so it made me confused.

Note that the answer is $1/(18\mathrm{ln}2)$