Question

Use your knowledge of the derivative to compute the value of the limit given below:
\lim_{h \rightarrow 0} \frac{\frac{1}{(x + h)^{7}} - \frac{1}{x^{7}}}{h} .

Answer 1

In your question I see only a description of a formula. Something has gone wrong with the equation editor. After pastig it back in the eq editor, I see this limit:\[\lim_{h \rightarrow 0} \frac{\frac{1}{(x + h)^{7}} - \frac{1}{x^{7}}}{h} \]This looks like the derivative of a certain function. I don't think you're supposed to expand the 7th degree polynomial...
Can you see what function it is?

Answer 2

the function is f(x)=1/x^7

Answer 3

-7x^-8