Question

Find the derivative of f(x) = -9/x at x = 12.

3/4
16
4/3
1/16

Answer 1

okay, this one is easy if you know how to derivate \[x^n\]

Answer 2

what you have to understand is that saying \[-9\div x\] is the same as\[(-9)1\div x\] and that \[(-9)* 1\div x=(-9)*x ^{-1}\]

Answer 3

and you know that \[(ax^n)'=nax ^{n-1}\]

Answer 4

in this case, a=-9 and n=-1

Answer 5

so, can you tell me the answer?

Answer 6

Where do I plug it in at?

Answer 7

see the formula I just posted

Answer 8

you have to use the one of \[(x^n)'=nx^{n-1}\]

Answer 9

Okay so I got -12

Answer 10

how did you get that??

Answer 11

see

Answer 12

\[(ax^n)'=nax ^{n-1}, -9=a, n=-1, (-9x ^{-1})'=(-1)(-9)x ^{-1-1}=9x ^{-2}\]

Answer 13

Oh so would it be 1/16?

Answer 14

hmmm see\[x ^{-2}=\frac{ 1 }{ x^2 }\]

Answer 15

so\[9x ^{-2}=\frac{ 9 }{ x^2 }\]

Answer 16

if x is 12 then it is 9/144

Answer 17

so yeah hahaha it's 1/16.... forgot to simplify xD