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Math Help - help finding the dirivative

  1. #1
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    help finding the dirivative

    Hi i am trying to find the dirivtive of (4-x^2)^(1/2). I know that i need to use u subsitution and u=4-x^2. Then i get d/dx[u^(1/2)](-2x) then i get stuck, can someone please help me?
    thank you
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  2. #2
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    Quote Originally Posted by cowboys111 View Post
    Hi i am trying to find the dirivtive of (4-x^2)^(1/2). I know that i need to use u subsitution and u=4-x^2. Then i get d/dx[u^(1/2)](-2x) then i get stuck, can someone please help me?
    thank you
    Chain rule: \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}.

    u = 4 - x^2.

    y = u^{1/2}.

    Therefore \frac{dy}{du} = \frac{1}{2} u^{-1/2} = \frac{1}{2} \frac{1}{\sqrt{u}} = \frac{1}{2} \frac{1}{\sqrt{4 - x^2}}\, and \frac{du}{dx} = -2x.

    So \frac{dy}{dx} = \frac{1}{2} \frac{1}{\sqrt{4 - x^2}} \times (-2x) = \frac{-x}{\sqrt{4 - x^2}}.
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  3. #3
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    awesome! thank you
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