设由方程x-y+1/2siny=0所确定的隐函数y=y(x)的一阶导数,
1个回答

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.