## anonymous 5 years ago 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

1. anonymous

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

2. anonymous

no, I dont have that option...

3. anonymous

no is that what you are asking

4. anonymous

oh, in the denominator, x+9 is squared

5. anonymous

oh squared not square root

6. anonymous

yeap

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

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

13. anonymous

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

14. anonymous

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