Question

Find the derivative of f(x) = -(9/x) at x = -8

Answer 1

so u can rewrite that as f(x)=-(9*x^(-1))
and when u find derivative of that just replace x for -8

Answer 2

but my options are
A. 8/9
B. 9/8
C. 64/9
D. 9/64

Answer 3

do you know how to find derivative of -(9*x^(-1))?

Answer 4

Don't I plug in (x+h) where x is?

Answer 5

ok so we need derivative of -(9/x)
1. we can plug out of the the -9 since its a constant and look for derivative of only 1/x
can u find derivative od 1/x?

Answer 6

ummm would it just be 1/-8?

Answer 7

ok so we can write 1/x as x^(-1) the derivative of that we can fine by the formula x^a=ax^(a-1) , so we would have -1*x^(-2) which is same as 1/x^2 and multiplied by the constant we put away before -9 it would be 9/x^2 now just replace for x=-8 in 9/x^2 and u have the answer

Answer 8

ohhhh, jeez why can't teachers just explain it that way. Its so much easier. Thanks so much man!

Answer 9

no problem

Answer 10

can you explain one more for me? well help me figure it out

Answer 11

yeah sure go ahead

Answer 12

Find the derivative of f(x) = -10x2 + 4x at x = 11.

Answer 13

my teacher told me the with the x I plug in (x+h)

Answer 14

is that true?

Answer 15

I kind of need a step by step with this one

Answer 16

um i dont really know the way with the plug in (x+h) if he told you probably its correct but cant remember really , if you want i can solve but not in that way

Answer 17

alright that would be fine, let me see what you get

Answer 18

its quite similar to the above using same formula if f(x)=x^a where a is any number then f'(x)=a*x^(a-1), so basicaly u need to use that twice for each term means for -10x^2 and +4x

Answer 19

so I plug in 11 at each x?

Answer 20

so lets go first for -10*x^2
same we can put the -10 aside since its constant and look for derivative of x^2

Answer 21

using the formula a*x^(a-1) for a=2 we would get 2*x^1 but we dont write the 1 so its only 2x

Answer 22

and since we put the -10 aside now we need to multiply it by -10 which leae us -20x for the first term

Answer 23

okay so now we have -20x + 4x?

Answer 24

no now you need to fine derivative of the second term means derivative of 4x

Answer 25

you do it same way but now for a=1 (because x is of degree 1)

Answer 26

so do you get 1 or do you get x^0?

Answer 27

so yeah for the x you would get x^0 which equals 1(since any number in power of 0 is 1)
but dont forget to multiply it with the constant 4

Answer 28

so now I have -20 + 4?

Answer 29

for the first one we had -20x , so you get -20x+4 , and now you only left to substitude for the value of x you need which was 11 i belive

Answer 30

oh so I just plug in the x now
so i get -220 + 44?

Answer 31

176 is my answer?

Answer 32

i dont know where u get the 44 from , because u dont have 4x you have only 4 so you dont multiply that by 11 so would leave you -220+4

Answer 33

oh yeahh its just 4... whoops! but thanks! that formula is really nice!

Answer 34

no problem , ur welcomed ^^