- #1

MrNeWBiE

- 75

- 0

**solve derivative by using the definition of the derivative limit ,,,**

hi alll

1. Homework Statement [/b]

find the derivative by using the definition of the derivative limit

h(x)= (x-1)^-2

3. The Attempt at a Solution

well ,,, first

f(x) = 1/(x-1)^2 ====> 1/(x^2-2x+1)

f(h+x) = 1/(x+h-1)^2 =====> 1/(x+h)^2-2hx+1 ===> 1/(x^2+2hx+h^2)-2hx+1

f(h+x)-f(x) = (1/x^2+h^2+1) - (1/x^2-2x+1) ===> x^2-2x+1-x^2+h^2+1/(x^2+h^2+1).(x^2-2x+1)

so it will be ,,,, -2x-h^2/x^4-2x^3+x^2 +(h^2.x^2)+2xh^2+h+x^2-2x+1

now adding the lim

lim(h=>0) (h^2+2x/x^4-2x^3+x^2 +(h^2.x^2)+2xh^2+h+x^2-2x+1)/h

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can someone tell me what did i do wrong so i can't divide the H down and the one up ,,,

i been trying to solve it from 2days ,,, =,=