Question

Find the derivative of f(x) = -7/x at x = -3.

Answer 1

I got 7/3 as the answer but it said its wrong

Answer 2

It may help you to re-write f(x) = -7/x as \[f(x)=-7x ^{-1}.\]

Answer 3

ok so, 1/-7x?

Answer 4

Focus on \[x ^{-1}\]. What's the derivative of \[x ^{-1}?\]

Answer 5

Hint: Use the Power Rule for Differentation.

Answer 6

\[\frac{ d }{ dx }x^n=nx ^{n-1}\]

Answer 7

So, \[\frac{ d }{ dx }x ^{-1}=?\]

Answer 8

never saw that before, online class skipped over it completely
Let me think

Answer 9

What is n in\[\frac{ d }{ dx }x ^{-1}~?\]

Answer 10

-1

Answer 11

so we get -1x^-2?

Answer 12

Again, this is the Power Rule for Differentiation. Yes, n=-1. Now, please find\[\frac{ d }{ dx }x ^{-1}\]

Answer 13

Yes, you have that correct.

Answer 14

But remember that your original problem began with "-7." You must keep that "-7".
So, what is your final result?

Answer 15

-7x^-2?

Answer 16

\[\frac{ d }{ dx }[-7x ^{-1}]=?\]

Answer 17

You have -7 as your coefficient, and your n is = -1. What is (-7)(-1)?

Answer 18

oops you're right, its +7x

Answer 19

Your +7 is correct, but your "x" is not.

Answer 20

\[\frac{ d }{ dx }[-7x ^{-1}]=?\]

Answer 21

You must use the "Power Rule for Differentiation."

Answer 22

+7x^-2

Answer 23

Yes, basically that's correct. I'd prefer that you write 7x^(-2), so that it is clear to the reader that your exponent is negative.

Now, let x=-3 in your final result.

Answer 24

Be certain to enclose your -3 inside parentheses: 7(-3)^(-2)=?

Answer 25

Note that you MUST do the exponentiation first here, and only then do the multiplication.

Answer 26

7*(-3)^(-2) = 7 * 1/9 = 7/9

Answer 27

beautiful.

Answer 28

thank you very much

Answer 29

my pleasure!