How would I use differentiation to go about solving this problem?

Question

"Consider the function h(x), for which h(4) = -1 and h'(4) = 4.

Find f'(4) for the function f(x) = h(x)/x."

I got this as f'(x) using the quotient rule: (x(h(x))'-h(x))/x^2

But I am not sure if this is right. And if it is right, I am not sure on how I can input 4 into the equation to get the answer I am looking for.

Any help?

Answer 1

So by quotient rule you have $$f'(x)= \frac{xh'(x)-h(x)}{x^{2}} \implies f'(4)=\frac{4\cdot h'(4)-h(4)}{4^2}$$