Question

Find the derivative of f(x) = 6/x at x = -2.
help

Answer 1

Rewrite f(x) so x is in the numerator. It'll be easier to take the derivative.

Answer 2

how do i do that

Answer 3

\[\Large\bf\sf f(x)\quad=\quad \frac{6}{x}\]Use this rule of exponents, as bunny mentioned.
\[\Large\bf\sf \frac{1}{x}\quad=\quad x^{-1}\]

Answer 4

so x^-6

Answer 5

Nooo you silly billy!\[\Large\bf\sf \frac{6}{x}\quad=\quad 6\frac{1}{x}\quad=\quad 6x^{-1}\]

Answer 6

Do you understand how I was able to pull the 6 out of the numerator like that?

Answer 7

i think so

Answer 8

but i don't get what to do after that

Answer 9

Power ruuuuule \c:/

Answer 10

Remember your power rule?

Answer 11

POWUH RULE IS THE BESTTT RULE.

Answer 12

One Power to Rule Them All!! \c:/

Answer 13

my guess is you are supposed to do this by hand, not power rule

Answer 14

do you put it under a radical

Answer 15

my guess is you have to compute
\[\lim_{x\to -2}\frac{f(x)-f(-2)}{x-(-2)}\]

Answer 16

does that look familiar?

Answer 17

How you not learned the shortcut rules at this point?
Still using the limit definition of derivative?
A little clarity would help ^^

Answer 18

would the answer be 3/2?

Answer 19

the derivative of \(\frac{1}{x}\) is \(-\frac{1}{x^2}\) so the derivative of \(\frac{6}{x}\) is \(-\frac{6}{x^2}\)

Answer 20

so i was right?

Answer 21

if \(x=-2\) you get \(-\frac{6}{(-2)^2}\) or \(-\frac{3}{2}\)

Answer 22

you were off by a minus sign

Answer 23

ohh.. darn. well thank you for helping :)