隐函数求导习题
问题描述:
隐函数求导习题
已知,f(x)为二阶可导的单值函数,f(1)=0,f’(1)=5,f"(1)=7.y=y(x)满足方程:f(x+y)=xy+x.求:dy/dx(x=0),d2y/dx2(x=0),
答
f(x+y)=xy+x中令x=0,得f(y)=0.因f(x)为二阶可导的单值函数,f(1)=0,故y=1.于是有x=0时y=1.f(x+y)=xy+x左右两边对x求导,得f'(x+y)*(1+y')=y+xy'+1 ①将x=0,y=1代入上式,有f'(1)*[1+y'(0)]=1+0+1也即5*[1+y'(0)]=2解得d...