Question

Find dz/dt for z=x^2 y+4y^2 where x=cost and y=sint using the chain rule

Answer 1

$\frac{dz}{dt}=x_tz_x+y_tz_y=(-\sin t)(2x)+(\cos t)(8y)=-2\sin t\cos t+8\cos t\sin t=$

$=6\cos t\sin t=3\sin 2t$