Question

Assume that for some function f(x), the expression f(x+h)-f(x) simplifies to -h/(x(x+h). Knowing this find f'(x). Then, what was f(x)?

I know this has to do with the limit of a derivative but I'm unsure how to proceed.

Answer 1

well have you found the limit as h->0 yet?

Answer 2

remember
\[\lim_{h \rightarrow 0}\frac{1}{h}(f(x+h)-f(x))=f'(x)\]

Answer 3

you have
\[f'(x)=\lim_{h \rightarrow 0}\frac{1}{h}(\frac{h}{x(x+h)})\]

Answer 4

evaluate the limit