Derive roots with multiple therms

Question

I have this function: $f(x)=\frac {x×\sqrt {-3x+9}}{2}$ Now I also tried to write it differently: $f(x)=\frac {x×(-3x+9)^\frac {1}{2}}{2}$ However I have no idea how I could derive it. Any help is appreciated.

Answer 1

Hint: By the chain rule and the product rule we get $$f'(x)=\frac{1}{2}\left((-3x+9)^{1/2}+x\frac{1}{2}(-3x+9)^{-1/2}(-3)\right)$$