Question

Find the derivative of f(x) = -11/x at x = 9.

Answer 1

Can you use the power rule to get the derivative of f(x)?

Answer 2

How would I do that?

Answer 3

-11/x = -11x^-1
now use the power rule

Answer 4

You can rewrite f(x) = -11x^(-1), is this a more recognisable form?

Answer 5

yes, thank you @aleroth ..
Okay, so... -1 \[-1 \times -11x ^{-2}\]

Answer 6

That you have now is the derivative of f(x), aka f'(x). The question wants you to plug in 9 into it as well to get the "derivative when x = 9"

Answer 7

so just plug in 9 for x? that's it?

Answer 8

Yep. Also just a note; f'(x) can also be written as 11/x^2. Know that 1/x = x^-1.

Answer 9

so the final answer should be 11/81? correct?

Answer 10

Yep

Answer 11

Thank you so much!!(:

Answer 12

Glad to help. :)