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Math Help - The bloody derivitives!

  1. #1
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    The bloody derivitives!

    What is the derivitive and method(of getting the derivitive) of
    f'(x)=-10/(3x+2)^2

    Thanks guys.
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  2. #2
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    As it's written, you must find f(x), perform integration.
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  3. #3
    Super Member angel.white's Avatar
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    Quote Originally Posted by Muhammed Ali View Post
    What is the derivitive and method(of getting the derivitive) of
    f'(x)=-10/(3x+2)^2

    Thanks guys.
    Initial equation
    f\prime (x)=-\frac{10}{(3x+2)^2}

    Take the derivative
    f\prime\prime(x)=\frac{d}{dx}\frac {-10}{(3x+2)^2}

    -10 is a coefficient, so we can write

    f\prime\prime(x)=-10\left[\frac{d}{dx}\frac 1{(3x+2)^2}\right]

    Then we rewrite without the fractions
    f\prime\prime(x)=-10\left[\frac{d}{dx}(3x+2)^{-2}\right]

    Use the product rule to move the negative 2 out front, and subtract 1 from the exponent making it negative 3, and the chain rule to take the derivative of the inside of the exponent.
    f\prime\prime(x)=-10(-2)(3x+2)^{-3}\left[\frac{d}{dx}(3x+2)\right]

    Use the power rule to turn d\dx(3x+2) into 3
    f\prime\prime(x)=-10(-2)(3x+2)^{-3}(3)

    Combine coefficients
    f\prime\prime(x)=60(3x+2)^{-3}

    Write as a fraction
    f\prime\prime(x)=\frac{60}{(3x+2)^3}
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  4. #4
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    Quote Originally Posted by Muhammed Ali View Post
    What is the derivitive and method(of getting the derivitive) of
    f'(x)=-10/(3x+2)^2

    Thanks guys.
    Are you saying you want to differentiate f'(x) to get f''(x).

    Or did you mean to say you want to integrate f'(x) to get f(x).
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  5. #5
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    Well, I got my first derivative wrong, so I'm dumb. But now I have everything figured out, thanks guys.
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