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Math Help - derivatives help

  1. #1
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    derivatives help

    Alright couple problems I'm having a bit of trouble with.

    If , then f ''(x) = ?

    and

    Suppose and i.e., and Also suppose That information implies
    and

    I'm just starting to understand getting the first derivative and so getting teh second derivative is kicking my butt. Then the second one have no clue who you would analyze that.

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  2. #2
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    Hello, UMStudent!

    If f(x) =9ln|sec(x) + tan(x)|, . find f''(x).
    I bet you didn't simplify the first derivative . . .


    . . . . . . . . sec(x)tan(x) + sec(x) . . . . . sec(x)[tan(x) + sec(x)]
    f'(x) .= .9 -------------------------- .= .9 --------------------------- .= .9sec(x)
    . . . . . . . . . . sec(x) + tan(x) . . . . . . . . . . sec(x) + tan(x)

    Then: .f''(x) .= .sec(x)tan(x)



    Suppose: F(x) = f(f(x)) .and .G(x) = [f(x)]

    Also suppose: f(4) = 5, f(5) = 2, f'(5) = 9, f'(4) = 10.

    Find F'(4) and G'(4).
    It's a matter of taking baby-steps . . .


    We have: .F(x) .= .f(f(x))

    . . Then: .F'(x) .= .f'(f(x))f'(x) . . . Chain Rule

    Hence: .F'(4) .= .f'(f(4))f'(4)
    . . . . . . . . . . . . . . . . .
    . . . . . . . . . .= . .f'(5) 10
    . . . . . . . . . . . . . .
    . . . . . . . . . .= . . .9 10 . = . 90


    We have: .G(x) .= .[f(x)]

    . . Then: .G'(x) .= .2f(x)f'(x)

    Hence: .G'(4) .= .2f(4)f'(4)
    . . . . . . . . . . . . . . . . .
    . . . . . . . . . .= . 2 5 10 . = . 100

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