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Math Help - Implicit Differentiation/Related Rates

  1. #1
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    Implicit Differentiation/Related Rates

    Question in manual:

    Variables x and y are functions of t.

    If (3x^2)y + 2x =2, and

    dy= -4 when x=2 and y=-3,
    dt

    then find dx
    sgggggggdt

    I can't isolate the equation for x, which is why I have to use the implicit differentiation, but I'm not sure how to set up the solution. Any ideas?
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  2. #2
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    Re: Implicit Differentiation/Related Rates

    Quote Originally Posted by Pewter12 View Post
    Question in manual:

    Variables x and y are functions of t.

    If (3x^2)y + 2x =2, and

    dy= -4 when x=2 and y=-3,
    dt

    then find dx
    sgggggggdt

    I can't isolate the equation for x, which is why I have to use the implicit differentiation, but I'm not sure how to set up the solution. Any ideas?
    you do not need to isolate x ... you need to isolate dx/dt after you take the time derivative.
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  3. #3
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    Re: Implicit Differentiation/Related Rates

    As a start, let's what your result is for the implicit differentiation. (This should be differentiation with respect to t.)
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    Re: Implicit Differentiation/Related Rates

    Thank-you for your replies. My question was not very clear. I understand the question is asking for dx/dt, and that taking the derivative of t comes first. Unfortunately I'm entirely confused as to how to the x=2 and y=-3 fit in, because the dx/dt format and derivatives in general are very new to me.
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  5. #5
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    Re: Implicit Differentiation/Related Rates

    \frac{d}{dt}\left(3x^2y + 2x = 2\right)

    note that the product rule is required for the first term ...

    3x^2 \cdot \frac{dy}{dt} + y \cdot 6x \cdot \frac{dx}{dt} + 2\frac{dx}{dt} = 0

    ... isolate \frac{dx}{dt} , sub in your given values and finish it.
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  6. #6
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    Re: Implicit Differentiation/Related Rates

    Thank-you, that is the clarification I was hoping for.
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