# What is the derivative of f(x)=sin(log_2(x)) ?

$f ' \left(x\right) = \cos \left({\log}_{2} x\right) \cdot \frac{1}{\left(\ln 2\right) x} = \frac{\cos \left({\log}_{2} x\right)}{\left(\ln 2\right) x}$
Note: $\left({\log}_{b} x\right) ' = \frac{1}{\left(\ln b\right) x}$