设z=f(x/y)且f为可微函数,则dz=
问题描述:
设z=f(x/y)且f为可微函数,则dz=
答
dz
=[偏f/偏(x/y)]·[偏(x/y) /偏x]dx + [偏f/偏(x/y)]·[偏(x/y) /偏y]dy
=[偏f/偏(x/y)]/y · dx - [偏f/偏(x/y)]·(x/y^2)· dy
答
dz=f'x(x/y)dx+f'y(x/y)dy=[f'(x/y)/y ]dx+f'(x/y) (-x/y²)dy