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Please show your process or work.

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Solution

T=x^2e^y-xy^3 dT/dt=2xe^ydx/dt+x^2e^ydy/dt-y^3dx/dt-3xy^2dy/dt dx/dt=-sint x=cost dy/dt=cost y=sint =e^(sint)(-2costsint+cos^2t sint)-sin^2t*2sintcost = e^(sint)sintcost(cost-2)-2sin^3tcost