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Math Help - derivative!

  1. #1
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    derivative!

    for f(x)=x*[1-4/(x+3)]

    what would be the easier way to solve this?
    put x into each equation then find derivative?
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  2. #2
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    Quote Originally Posted by nuclear123 View Post
    for f(x)=x*[1-4/(x+3)]

    what would be the easier way to solve this?
    put x into each equation then find derivative?
    f(x) = x\left(1 - \frac{4}{x + 3}\right)

     = x\left[1 - 4(x + 3)^{-1}\right].


    Now use the product rule.

    f'(x) = x\left[1 - 4(x + 3)^{-1}\right]' + \left[1 - 4(x + 3)^{-1}\right](x)'

     = x \cdot 4(x + 3)^{-2} + \left[1 - 4(x + 3)^{-1}\right]\cdot 1

     = \frac{4x}{(x + 3)^2} + 1 - \frac{4}{x + 3}.
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