1.求由方程ey=x2siny+cosx所确定的隐约数y=y(x)的微分dy2.设函数y=ex2,求y’’/x=0

Question

1.求由方程ey=x2siny+cosx所确定的隐约数y=y(x)的微分dy 2.设函数y=ex2,求y’’/x=0

Answer 1

1.求由方程e^y=x^2siny+cosx所确定的隐约数y=y(x)的微分dy
两边同时对x求导,得：
e^y*dy=2xsiny+x^2*cosy*dy-sinx
(e^y-x^2*cosy)dy=2x*siny-sinx
dy=(2x*siny-sinx)/(e^y-x^2*cosy)

2.设函数y=e^(x^2),求y’’/x=0
y'=e^(x^2)*2x
y''=e^(x^2)*2x*2x+2e^(x^2)
=(4x^2+2)*e^(x^2)

当x=0时,
y''=2