设z=ln(x+y2)且x=et，y=t2，则dz/dt=____．

设z=ln(x+y²)且x=e^t，y=t²，则dz/dt=____．
【正确答案】：e^t+4t³/e^t+t⁴。 解析：dz/dt=z/x•dx/dt+z/y•dy/dt=1/(x+y²)•e^t+2y/(x+y²) •2t=e^t+4t³/e^t+t⁴