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Please show your work or process.

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Solution

well
dT/dt=dT/dx*dx/dt+dT/dy*dy/dt
is just the chain rule for function T of two variables. There is nothing to show

T(x,y)=x²e^y-xy³

x=cos(t)

y=sin(t)

dT/dx=2xe^y-y³ (we treat y as a constant)

dx/dt=-sin(t)

dT/dy= x²e^y-3xy² (we treat x as a constant, derivative of e^y is e^y)

dy/dt=cos(t)

Putting all together

dT/dt=dT/dx*dx/dt+dT/dy*dy/dt

=(2xe^y-y³)(-sin(t))+(x²e^y-3xy²)cos(t)