Question

Find the derivative of f(x) = -3/x at x = -4.

Answer 1

that's not an option, my options are
3/4
4/3
16/3
3/16

Answer 2

oh i see, do you want to show how to get the answer (3/16)?

Answer 3

yes please!

Answer 4

Do you know the power rule?

Answer 5

I know it but i'm confused how to use it

Answer 6

and I thought with fractions, you couldnt use it

Answer 7

first of we have -3/x
we need to put the x in the numerator to use the power rule

Answer 8

so multiply by -x on top and bottom?

Answer 9

when we switch the x to the numerator, it will be x^-1
so it will be -3x^-1

Answer 10

okay

Answer 11

think of it as a reciprocal

Answer 12

now we use the power rule, do you the formula?

Answer 13

d/dx ^xn= nx^n-1

Answer 14

yes! i learned better way
if you use the f'(x)= cnx^n-1
where c= constant
n= exponent

Answer 15

its pretty much the same thing

Answer 16

-3x^-1
use the power rule, we have
-3(-1)x^-1-1

Answer 17

then simplify that and sub in the -4 into x

Answer 18

-4^-2
-4/x^2?

Answer 19

-3(-1) multiply = 3x^-2

Answer 20

oh, and then plug in -4?
so: 3(-4)^2???

Answer 21

yes, remember the the negative sign, change to the reciprocal
it wil be 3(1/(-4^2))

Answer 22

3(1/16)

Answer 23

f'(x)= 3/16

Answer 24

thank you so much!

Answer 25

glad i could help! :)