Question

HELP: Use your knowledge of the derivative to compute the limit given below:

The derivative that is being calculated is

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

^

Answer 5

yes

Answer 6

im not sure how to start this

Answer 7

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.

Answer 8

right i used the power rule.

Answer 9

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

Answer 10

-6/x^7

Answer 11

Right.

Answer 12

^_^