Question

Find the Derivative of f(x)=-6/x at x=12

Answer 1

@AriPotta Can you help me out on this?

Answer 2

I can show you guys the work I have so far if you want

Answer 3

yes do that

Answer 4

-6x/x(x+h)-(-6(x+h)/x(x+h))

Answer 5

I believe I am making a mistake at that step

Answer 6

i see - its derivation form first principles

Answer 7

Yep

Answer 8

oops - i'll have to do a little revision on that ...

Answer 9

From there I would get (-6x-(-6x-6h))/h

Answer 10

if no one can help - i;ll be back in about 5-10 minutes

Answer 11

alrighty

Answer 12

I eentually get that it equals 6 but the answer choices are 12, 1/2, 1/24, or 2.

Answer 13

You guys have anything?

Answer 14

ok - i remember now lol!
but johnweldon1993 is answering..

Answer 15

No go right ahead, I'm actually stuck on the last step XD

Answer 16

Oh I feel stupid XD

Answer 17

I think I'm gonna go with the wild guess of 24

Answer 18

Oh the terrible beginning!! lol

\[\large \lim_{h -> 0}\frac{f(x + h) - f(x)}{h}\]

So since we know f(x) = -6/x...so we plug that in here

\[\large \frac{\frac{-6}{x + h} - \frac{-6}{x}}{h}\]

We need our common denominator on the top which you found to be x(x + h)

\[\large \frac{\frac{-6x - (-6(x + h)}{x(x + h)}}{h}\]
\[\large \frac{\frac{\cancel{-6x + 6x} + 6h}{x(x + h)}}{h}\]

So we have
\[\large \frac{\frac{6h}{x(x + h)}}{h} \]

re-write it as

\[\large \frac{6h}{hx(x + h)}\]

Cancel out your 'h'

\[\large \frac{6\cancel{h}}{\cancel{h}x(x + h)}\]

\[\large \lim_{h->0}\frac{6}{x^2 + h}\]

what does that equal?

Answer 19

set x=12 and h=0 and you get 1/24

Answer 20

good work

Answer 21

And you are correct!

Answer 22

I see what I did wrong I took out the common denominator...

Answer 23

Thanks guys!

Answer 24

It wont allow me to close the question...