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Math Help - Implicit Differentiation Help finding the derivative of this function.

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    Implicit Differentiation Help finding the derivative of this function.

    Find the derivative of sqrt x = 5 x sqrt y


    Answer in the back of the book doesnt make sense to me. d/dx = 1/25

    HELPPP!!!!
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    Re: Implicit Differentiation Help finding the derivative of this function.

    Quote Originally Posted by Mathinik View Post
    Find the derivative of sqrt x = 5 x sqrt y


    Answer in the back of the book doesnt make sense to me. d/dx = 1/25

    HELPPP!!!!
    Is it \displaystyle \begin{align*} \sqrt{x} = 5x\,\sqrt{y} \end{align*} or \displaystyle \begin{align*} \sqrt{x} = 5 \times \sqrt{y} \end{align*}?

    Also, were you asked to find the derivative at a POINT, or just the derivative?
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    Re: Implicit Differentiation Help finding the derivative of this function.

    times. we were asked to find the derivative
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    Re: Implicit Differentiation Help finding the derivative of this function.

    So it's \displaystyle \begin{align*} \sqrt{x} = 5\sqrt{y} \end{align*}. Solving for y gives

    \displaystyle \begin{align*} \sqrt{y} &= \frac{1}{5}\sqrt{x} \\ y &= \frac{1}{25} x \\ \frac{dy}{dx} &= \frac{1}{25} \end{align*}
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    Re: Implicit Differentiation Help finding the derivative of this function.

    Quote Originally Posted by Prove It View Post
    So it's \displaystyle \begin{align*} \sqrt{x} = 5\sqrt{y} \end{align*}. Solving for y gives

    \displaystyle \begin{align*} \sqrt{y} &= \frac{1}{5}\sqrt{x} \\ y &= \frac{1}{25} x \\ \frac{dy}{dx} &= \frac{1}{25} \end{align*}



    My instructor said to not solve for y and do what we nomrmally do, take the derivative of each term wit respect to x, and treat y like an x and multiply it with dy/dx.
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    Re: Implicit Differentiation Help finding the derivative of this function.

    Quote Originally Posted by Mathinik View Post
    My instructor said to not solve for y and do what we nomrmally do, take the derivative of each term wit respect to x, and treat y like an x and multiply it with dy/dx.
    Then your instructor is a Goober for making you do something the long way when there is very clearly a much simpler way to go about it. You should use Implicit Differentiation ONLY when it would be easier than trying to solve for y and taking the derivative explicitly.
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    Re: Implicit Differentiation Help finding the derivative of this function.

    so (sqrt y) / (5(sqrt x)) would still be correct if i use implicit differentiation?
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    Re: Implicit Differentiation Help finding the derivative of this function.

    Quote Originally Posted by Prove It View Post
    Then your instructor is a Goober for making you do something the long way when there is very clearly a much simpler way to go about it. You should use Implicit Differentiation ONLY when it would be easier than trying to solve for y and taking the derivative explicitly.

    so (sqrt y) / (5(sqrt x)) would still be correct if i use implicit differentiation?
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    Re: Implicit Differentiation Help finding the derivative of this function.

    Quote Originally Posted by Mathinik View Post
    so (sqrt y) / (5(sqrt x)) would still be correct if i use implicit differentiation?
    You would be expected to fully simplify it.
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