Question

Find the derivative of f(x) = 8 divided by x at x = -1.

4
0
8
-8
@ganeshie8 @hero @dan815 @perl @pooja195 @solomonzelman @mathstudent55 @zepdrix @usukidoll @

Answer 1

Remember your exponent rule? :)\[\Large\rm \frac{1}{x}=x^{-1}\]

Answer 2

no i dont; i dont know anything

Answer 3

\[\Large\rm f(x)=\frac{8}{x}\]Applying this exponent rule,\[\Large\rm f(x)=8x^{-1}\]

Answer 4

Then simply apply your power rule to take derivative! :)
The -1 comes down to multiply, then subtract 1 from the exponent. ya?

Answer 5

would it be 8? @zepdrix

Answer 6

Hmm no :o

Answer 7

how'd you get 8?

Answer 8

wait never mind, why would i subtract?

Answer 9

\[\Large\rm f(x)=x^n\]Power rule tells us how to deal with polynomials,\[\Large\rm f'(x)=nx^{n-1}\]

Answer 10

Example:\[\Large\rm g(x)=4x^{3}\qquad\to\qquad g'(x)=4\cdot3x^{3-1}\]\[\Large\rm g'(x)=12x^{2}\]

Answer 11

you don't know anything? +_+
lol that's not good

Answer 12

i dont please help? @zepdrix
can u take me step by step with my example

Answer 13

Nooo I don't wanna give you the answer :D
I think you can do it.

Let's work on a problem that's very similar.
Given that \(\large\rm f(x)=\frac{4}{x^{2}}\) find f'(x) at x=2.
We'll first write f(x) differently using our exponent rule,\[\large\rm f(x)=4x^{-2}\]Then we'll apply our power rule to take our derivative:
The -2 comes down in front, and then we subtract 1 from the exponent:\[\large\rm f'(x)=4\cdot(-2)x^{-2-1}\]\[\large\rm f'(x)=-8x^{-3}\]Let's apply our exponent rule in reverse, putting the x back into the bottom,\[\large\rm f'(x)=\frac{-8}{x^3}\]Evaluating this function at x=2 gives us:\[\large\rm f'(2)=\frac{-8}{2^3}\]\[\large\rm f'(2)=-1\]

Answer 14

yayyy :) there are some stepssss

Answer 15

When you apply your power rule, be careful when dealing with negative exponents!

If we have a -1 exponent, subtracting 1 from that will not give us 0,
it will give us -2

Answer 16

im not asking for the answer I'm just trying to go step by step with my example with you

Answer 17

@zepdrix

Answer 18

so next would be f(x)=8x

Answer 19

@zepdrix

Answer 20

no, we have 8x^(-1)
:O it gains a power of -1 when it comes up

Answer 21

Then apply your power rule,
the -1 comes down in front as a multiplier, and the power decreases to -2.\[\large\rm f'(x)=8(-1)x^{-2}\]Simplify before plugging in your value,\[\large\rm f'(x)=\frac{-8}{x^2}\]

Answer 22

Then plug in your -1 :)

Answer 23

so then its f(x)=-8/-1^2

Answer 24

what do i do next? @zepdrix

Answer 25

\[\large\rm f'(-1)=\frac{-8}{(-1)^2}\]ya, then simplify.

Answer 26

them it will be f(x)=-8/1 right? @zepdrix

Answer 27

so the answer would be 8? @zepdrix

Answer 28

-8/1 does not equal 8

Answer 29

so is the answer -8?

Answer 30

@zepdrix

Answer 31

but would f(-1)=-8/-1^2=8? @zepdrix

Answer 32

yes :)

Answer 33

-8

Answer 34

when you square -1, you get 1.

Answer 35

can you help me with another? @zepdrix

Answer 36

Find the derivative of f(x) = -12x2 + 9x at x = 6.

-112.5
-135
-90
-108
@zepdrix