Question

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

Answer 1

@Jhannybean @ivancsc1996

Answer 2

What formulas of derivation do you know?

Answer 3

\[\large f(x)=\frac{2}{x}\]\[\large f(x)=2x^{-1}\] for starters.

Answer 4

Do you know the formula to derive 1/x?

Answer 5

Now can you find the derivative?

Answer 6

Or the power formula?

Answer 7

uhhhhhh Okay lemme see

Answer 8

to find the derivative here, you can follow the format \[\large\frac{nx^{n-1}}{(n-1)}\]

Answer 9

-4^-1 = 1/4

Answer 10

POWER RULE WITH RATIONAL EXPONENTS. DONE.

Answer 11

Lol for confidence, genius, you get best response. Except I don't know what to do with that lol

Answer 12

\[\large x^{-1}\] your -1 is your n. \[\large \frac{-1\cdot x^{-1-1}}{-1-1}\]

Answer 13

-1*x^-2 / 1

Answer 14

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

Answer 15

oh -2!

Answer 16

Now you have a 2 multiplying this.

Answer 17

-4^2 = 16 so then 1/16

Answer 18

uhhh this is hard >:(

Answer 19

So you'll have \[\large 2\cdot \frac{1}{2x^2}= \frac{1}{x^2}\]

Answer 20

\[\large f'(-2) = \frac{1}{(-2)^2}=?\]

Answer 21

2*1/16 = 1/8 = 1/4

Answer 22

thats 1/4

Answer 23

good job!

Answer 24

but jhanny somethings wrong. My options are only 1, 1/2, -1/2, and -1

Answer 25

O_o

Answer 26

lol

Answer 27

idk what went wrong. I think i might have multiplied or something wrong

Answer 28

Oof.one minute. I'll writeout what i did.

Answer 29

okay thx

Answer 30

\[f(x)=2x^{-1}\]\[f'(x) = 2(-1)x^{-2}= -2\cdot \frac{1}{x^2} =-\frac{2}{x^2}\]

Answer 31

Look at it this way. You need to find the rate of change of 2/x. This is:\[\frac{ d }{ dx }2/x\]Since 2 doesnt change, then you can take it out:\[\frac{ d }{ dx }2/x=2\frac{ d }{ dx }1/x\]Now, the formula for deifferentiating 1/x is \[\frac{ d }{ dx }1/x=-\frac{ 1 }{ x ^{2}} \rightarrow 2\frac{ d }{ dx }1/x=-\frac{ 2 }{ x ^{2} } \rightarrow ANS=-\frac{ 2 }{ (-2)^{2} }=-\frac{ 1 }{ 2 }\]

Answer 32

-2/4 = -1/2

Answer 33

Ah... wasnt supposed to get rid of the 2. my bad.