Question

can someone help me do this please?
- Using the definition lim h->0 f(x+h) - f(x)/h, to find the derivative at x.
f(x)= 8/(x+9)^2

Answer 1

is it \[8\div(\sqrt{x+9})\]

Answer 2

no, I dont have that option...

Answer 3

no is that what you are asking

Answer 4

oh, in the denominator, x+9 is squared

Answer 5

oh squared not square root

Answer 6

yeap

Answer 7

well just taking the derivative it should be -16/(x+9)^3

Answer 8

step 1: lim h--> 0 [8/(x+h+9)^2 - 8/(x+9)^2]/h

Answer 9

factor the top, and cancel out all the terms, you should have a factor of "h" in every term in the numberator

Answer 10

it's tedious.. but i simplify to ...

Answer 11

when i factor the denominator, i gont get an h in every term

Answer 12

-8(2xh+18h+h^2)/[h*((x+h+9)^2)(x^2+18x+81)]

Answer 13

cancel the h, you get -8(2x+18+h)/[((x+h+9)^2)(x^2+18x+81)]

Answer 14

in the limit as h--> , this reduces to -16x/(x+9)^3