anonymous 3 years ago HELP: Use your knowledge of the derivative to compute the limit given below: The derivative that is being calculated is

1. anonymous

2. anonymous

im confused. am i suppose to use the power rule or quotient rule to find the derivative?

3. asnaseer

do you know how to write the general form for the derivative of f(x)?

4. anonymous

It sounds like the problem is asking you to recognize that the given limit is the definition of the derivative of some function. Given $$\displaystyle\lim_{h\to0}\dfrac{f(x+h)-f(x)}{h}$$, find $$f(x)$$. Then, simply compute the derivative.

5. asnaseer

^

6. anonymous

yes

7. anonymous

im not sure how to start this

8. anonymous

Well do you know how to find the derivative? The way the question is stated makes it sound like you've learned some of or all the "rules" for differentiation. In this case, since $$f(x)=\dfrac{1}{x^6}$$, you would apply the power rule to find the derivative, and that would be your answer.

9. anonymous

right i used the power rule.

10. anonymous

Okay, so that gives you $f(x)=\frac{1}{x^6}=x^{-6}~\Rightarrow~f'(x)=\cdots$

11. anonymous

-6/x^7

12. anonymous

Right.

13. anonymous

^_^