设z=uv+sint,而u=e',v=cost,求dz/dt

问题描述:

设z=uv+sint,而u=e',v=cost,求dz/dt

dz/dt=dz/du*du/dt+dz/dv*dv/dt+dz/dt
=v*e^t-usint+cost
=e^t(cost-sint)+cost