Question

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

Answer 1

@mathslover

Answer 2

Would I use the power rule?

Answer 3

Yup, 7 is a constant. So, it has nothing to do with differentiation. Just keep it out for once, and differentiate 1/x

Answer 4

Oh and yes, don't forget that "-1" .

\(\cfrac{d}{dx} \left(\cfrac{-7}{x}\right) = -7 \cfrac{d}{dx} \left( \cfrac{1}{x}\right) = -7 \cfrac{d}{dx} \left(x^{-1}\right) \)

This is what I mean.

Answer 5

Just use the power rule now : \(\cfrac{d}{dx} x^n = nx^{n-1} \)

Let me know what you get.

Answer 6

\(-7x^{-2}\)?

Answer 7

Check the sign! (in front of 7)

Answer 8

7x^-2 ?

Answer 9

Yep! Now plug-in x = -3

Answer 10

wait, isn't there a rule or something for negative exponents?

Answer 11

No, there isn't any specific, as far as my knowledge is concerned.

http://www.wolframalpha.com/input/?i=differentiate+-7%2Fx

The answer is same, so, don't worry, you're going right.

Answer 12

7(-3)\(^{-2}\)

Answer 13

Yeah, that's correct! Good work.

Answer 14

:D
what's after that?

Answer 15

find it :)

Answer 16

Uhmm.. simplify? And then party? :O :P

Answer 17

xD

Answer 18

7/9!

Answer 19

jess i have a tutorial on derivatives
you can just revise that ;)

Answer 20

:O

Answer 21

I didn't know that!

Answer 22

correct
All The Best :)

Answer 23

Is the post showing closed for you guys?

Answer 24

yes