Math Help - Derivatives

1. Derivatives

Directions: Find the derivaive of f(x) at x.
f(x)= 1/(x+2) x= -1

I used the formula f^1(x)= Limit as h approaches 0 [f(x+h) - f(x)]/h

And now I'm at [ 1/(x+h+2) - 1/(x+2) ] /h

I would appreciate any help.

2. Originally Posted by Purpledog100
Directions: Find the derivaive of f(x) at x.
f(x)= 1/(x+2) x= -1

I used the formula f^1(x)= Limit as h approaches 0 [f(x+h) - f(x)]/h

And now I'm at [ 1/(x+h+2) - 1/(x+2) ] /h

I would appreciate any help.
From there, combine the fractions to get $\lim_{h\to0}\frac{x+2-(x+h+2)}{h(x+2)(x+h+2)}=\lim_{h\to0}\frac{-h}{h(x+2)(x+h+2)}=\dots$

Can you continue?

3. Do the instructions specify that you need to use the limit definition of the derivative? If not, just use the power rule.

$\frac{dy}{dx}=-\frac{1}{(x+2)^{2}}$

$\frac{dy}{dx}(-1)=-\frac{1}{(-1+2)^{2}}=-\frac{1}{(1)^{2}}=-1$