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Math Help - derivative question.

  1. #1
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    derivative question.

    if f in sqrt(f(x)) is differentiable, would it equal to

    f'(x)
    ------
    2sqrt[f(x)] ?
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  2. #2
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    trying this out with x^3, i get 2(x^3)-1*(3x^2), and i think this would yield....

    3x^2
    ------
    2(x^3)

    I know this is a dumb simplification problem but i just wanted some clarification. thanks.
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  3. #3
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Evan.Kimia View Post
    if f in sqrt(f(x)) is differentiable, would it equal to

    f'(x)
    ------
    2sqrt[f(x)] ?
    Let y = \sqrt{f(x)}

    y^2 = f(x)

    2y\frac{dy}{dx} = f'(x)

    \frac{dy}{dx} = \frac{f'(x)}{2y} = \frac{f'(x)}{2\sqrt{f(x)}}

    I get the same answer as you but I'm not 100% confident it's right
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  4. #4
    MHF Contributor ebaines's Avatar
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    Quote Originally Posted by Evan.Kimia View Post
    trying this out with x^3, i get 2(x^3)-1*(3x^2), and i think this would yield....

    3x^2
    ------
    2(x^3)

    I know this is a dumb simplification problem but i just wanted some clarification. thanks.
    Not quite right. You should have:

    <br />
f(x) = \sqrt {x^3}<br />
    <br />
f'(x) = \frac {3x^2} {2 \sqrt{x^3}} = \frac 3 2 \sqrt x<br />

    An easier way is to realize that
     \sqrt {x^3} = x^{3/2}<br />

    So you get right to:
    <br />
f'(x) = \frac 3 2 x^{1/2} = \frac 3 2 \sqrt x<br />
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