Question

设由方程x-y+1/2siny=0所确定的隐函数y=y(x)的一阶导数,

Answer 1

x-y+1/（2siny）=0
(x-y)*2siny+1=0
x*2*siny-y*2*siny+1=0
x*2*siny+1=y*2*siny
两边微分：
d[x*2*siny+1]=d[y*2*siny]
2*[siny*dx+x*cosy*dy]=2*[dy*siny+y*cosy*dy]
[siny]*dx=[siny+y*cosy-x*cosy]dy
dy/dx=[siny]/[siny+y*cosy-x*cosy]
如果题目是：x-y+0.5*siny=0
两边微分：
d[x-y+0.5*siny]=d0
dx-dy+0.5*cosy*dy=0
dx=[1-0.5*cosy]dy
dy/dx=1/[1-0.5*cosy]=2/[2-cosy]
对于类似的隐函数求导,要善于用微分法,这样X与Y处于平等地位,容易理解也容易做题.