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Math Help - Derivatives

  1. #1
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    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.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Purpledog100 View Post
    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?
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  3. #3
    Senior Member Pinkk's Avatar
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    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
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