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Math Help - Total derivative

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    Total derivative

    Find the total derivative dQ/dt, where Q = (x^2 + 4y^3) sin(2t^3), and x = t^3, y = t^2, expressing your final answer in terms of t alone (no x or y terms).

    What is the value of dQ/dt?
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  2. #2
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    Q=(t^4+4t^6)sin(2t^3)

    Q=t^4(1+4t^2)sin(2t^3)

    \frac{dQ}{dt}=4t^3(1+4t^2)sin(2t^3)+8t^5sin(2t^3)+  6t^6(1+4t^2)cos(2t^3)
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    Quote Originally Posted by mr_motivator View Post
    Find the total derivative dQ/dt, where Q = (x^2 + 4y^3) sin(2t^3), and x = t^3, y = t^2, expressing your final answer in terms of t alone (no x or y terms).

    What is the value of dQ/dt?
    Use

    \frac{dQ}{dt}=\frac{\partial Q}{\partial x}\frac{dx}{dt}+\frac{\partial Q}{\partial y}\frac{dy}{dt}

    and then substitute for x and y. Or substitute first and differentiate like normal.
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