解dOz.+0z.cDz dt au dt a Dy dt at ve-usint+ cost =e cost-e sint cost e(cost-sin t)+cost. 例3设W=f(a,"),=(x,y),"=v(x,y) x=x(r,6),y=y(r,6) 均满足复合函数求偏导数的条件计算 ar a0 (两重复合问题) 解由链式法则 X y 6解 t z dt dv v z dt du u z dt dz + + = ve u t t t = − sin + cos e t e t t t t = cos − sin + cos e (cost sin t) cost. t = − + 例3 设 ( , ), ( , ) ( , ), ( , ), ( , ), x x r y y r w f u v u u x y v v x y = = = = = 均满足复合函数求偏导数的条件 计算 w r w , (两重复合问题) 解 由链式法则 w u v x y r