求一函数的偏导数和全微分设f(x,y)=sin(xy)+cos(y/x)具有一阶偏导数,求函数f(x,y)的偏导数和全微分.有没有人知道怎么做,
问题描述：
求一函数的偏导数和全微分
设f(x,y)=sin(xy)+cos(y/x)具有一阶偏导数,求函数f(x,y)的偏导数和全微分.
有没有人知道怎么做,
答
f'x=ycos(xy)-sin(y/x)(-y/x²)=ycos(xy)+(y/x²)sin(y/x)
f'y=xcos(xy)-(1/x)sin(y/x)
df=f'xdx+f'ydy=[ycos(xy)+(y/x²)sin(y/x)]dx+[xcos(xy)-(1/x)sin(y/x)]dy