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Math Help - Related Rates / Implicit Differentiation

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    Related Rates / Implicit Differentiation

    I'm so lost with this question:

    If y = x^2 + 4x and dx/dt = 10 find dy/dt when x = 5.

    Can someone help me with this question please?
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    Quote Originally Posted by millerst View Post
    I'm so lost with this question:

    If y = x^2 + 4x and dx/dt = 10 find dy/dt when x = 5.

    Can someone help me with this question please?
    You can use the chain rule:

    \frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx}

    You know dt = 0.1 and dy/dx should be easy to find
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    Quote Originally Posted by millerst View Post
    I'm so lost with this question:

    If y = x^2 + 4x and dx/dt = 10 find dy/dt when x = 5.

    Can someone help me with this question please?
    \frac{d}{dt}(y = x^2 + 4x)

    \frac{dy}{dt} = 2x\frac{dx}{dt} + 4\frac{dx}{dt}

    \frac{dy}{dt} = \frac{dx}{dt}(2x+4)

    substitute in your given values for x and \frac{dx}{dt} to find the value for \frac{dy}{dt}
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    Sketter, what happened to the dy/dx?
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  5. #5
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    Quote Originally Posted by millerst View Post
    Sketter, what happened to the dy/dx?
    there is no \frac{dy}{dx} ... the derivative was taken with respect to t ... that's what the \frac{d}{dt} in front of the equation means.
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