设z=f(y/x)且f是可微函数,求全微分dz
问题描述:
设z=f(y/x)且f是可微函数,求全微分dz
答
我用z_x表示z对x的偏导数,其他类似:
dz = z_x dx + z_y dy,
z_x = f'(y/x) (-y/x^2),z_y = f'(y/x)/x,于是
dz = - y f'(y/x) / x^2 dx + f'(y/x) / x dy