Answer
See explanations.
Work Step by Step
Given the equation $T=2\pi\sqrt {\frac{L}{g}}$ and $\frac{dL}{du}=kL$, we have
$\frac{dT}{du}=\frac{dT}{dL}\frac{dL}{du}=2\pi(\frac{1}{2}\frac{1}{\sqrt {gL}})kL=\frac{k}{2}(2\pi\sqrt {\frac{L}{g}})=\frac{kT}{2}$
