Question

Find the derivative of f(x) = negative 11 divided by x at x = 9.

Answer 1

I am completely lost here

Answer 2

What is the function: \(\large\color{black}{ f(x)=\frac{\LARGE 11}{\LARGE x} }\) ?

Answer 3

And you need the derivative when x=9, all that means is \(\large\color{black}{ f'(9) }\).

Answer 4

I will rewrite the function for you, and you will apply the power rule.

\(\large\color{black}{ f(x)=11\cdot x^{-1} }\) Can you differentiate this?

Answer 5

Wouldnt you just input the 9 in the x spot?

Answer 6

not to plug in 9 for x into the \(\large\color{black}{ f(x) }\), but into the \(\large\color{black}{ f'(x) }\).

Answer 7

They aren't asking you to differentiate a constant.... it won't be hard:)

Answer 8

Okay. Can you explain what you man when you say differentiate?

Answer 9

`to differentiate` means `to take the derivative`.

Answer 10

What is troubling you?

Answer 11

Im not sure how to start this...

Answer 12

okay, if I were to ask you what the derivative of \(\large\color{brown}{ x^{-1} }\) would you be able to tell me?

Answer 13

I think the term derivative is confusing me... is there another word for it?

Answer 14

\(\large\color{brown}{ \frac{\LARGE d }{\LARGE dx}x^{\rm n}={\rm n}{\tiny ~}x {\tiny ~}^{{\rm n}-1} }\). (in your case, \(\large\color{brown}{{\rm n} }\) is -1)

Answer 15

what is d?

Answer 16

\(\large\color{brown}{ \frac{\LARGE d }{\LARGE dx} }\) is a notation for a derivative

Answer 17

Okay. Let me see If i can figure this out

Answer 18

\(\large\color{brown}{ \frac{\LARGE d }{\LARGE dx}x^{\rm \color{blue}{n}}={\rm \color{blue}{n}}{\tiny ~}x {\tiny ~}^{{\rm \color{blue}{n}}-1} }\)

\(\large\color{brown}{ \frac{\LARGE d }{\LARGE dx}x^{\rm \color{blue}{-1}}={\rm \color{blue}{(-1)}}{\tiny ~}x {\tiny ~}^{{\rm \color{blue}{(-1)}}-1} }\)

Answer 19

So i would just plug and solve for x?

Answer 20

tell me the derivative of x^-1 in most simplified terms first

Answer 21

\(\large\color{brown}{ \frac{\LARGE d }{\LARGE dx}x^{\rm \color{blue}{-1}}={\rm \color{blue}{(-1)}}{\tiny ~}x {\tiny ~}^{{\rm \color{blue}{(-1)}}-1}=-x^{-2}=-1/x^2 }\)

Answer 22

so \(\large\color{brown}{ f'(x)=-1/x^2 }\)

and for any real number a, \(\large\color{brown}{ f'(a)=-1/(a)^2 }\)