Recurrence relation of Chebyshev nodes

Question

Doing a few practice questions, I came across a proof based question. How would one go around to solve this?

"Prove the following recurrence relation:"

$\frac{d}{dx}T_{n+1}(x)=(n+1)T_n(x)+\frac{n+1}{n}x\frac{d}{dx}T_n(x)$

for $n=1,2,3...$