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Math Help - chain rules

  1. #1
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    chain rules

    z=x^2y+xy^2
    x=5+t^5
    y=-2+t^2
    how to find dz/dt?
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  2. #2
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    \frac{dz}{dt} = x^2\frac{dy}{dt} + 2xy\frac{dx}{dt} + 2xy\frac{dy}{dt} + y^2\frac{dx}{dt} = x^2\frac{dy}{dt} + 2xy\left(\frac{dx}{dt} + \frac{dy}{dt}\right) + y^2\frac{dx}{dt}

    x = 5+t^5

    \frac{dx}{dt} = 5t^4

    y = t^2 - 2

    \frac{dy}{dt} = 2t

    if you want \frac{dz}{dt} in terms of t, perform the substitutions.
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  3. #3
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    10t+20t^3-80t^4+56t^6+4t^8-20t^9+10t^11is it the right answer?
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  4. #4
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    I don't know ... I left the grunt work algebra to you.
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