Calculus

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Find a formula for the derivatives of the function m(x)=1/(x+1)

IS the answer -1/(x+h)(x+h+1)

  • Calculus -

    [(x+1)(0) - 1(1)]/(x+1)^2
    =-1/(x+1)^2
    =-1/(x^2+2x+1)
    now doing it as a limit you must let h go to zero
    [f(x+h) -f(x)]/h as h -->0
    [1/(x+h+1)-1/(x+1)]/h
    [(x+1)-(x+h+1)]/[h(x+h+1)(x+1)]
    -1/(x+h+1)(x+1)
    as h -->0
    -1/[(x+1)(x+1)]
    -1/(x^2+2x+1) as we knew

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