Question

1 求下列函数的微分 求详细步骤

Answer 1

微分和导数一样
(1)y=x^3+2x^2-3
dy=3x2dx+4dx=(3x2+4)dx
(2)y=e^(-x)sinx
dy=[－e(－x)]dx
sinx
+e（－x）cosxdx
=
e（－x）(-sinx+cosx)dx
(3)y=(x+1)/(x-1)
dy=(x-1)
dx
+(x+1)
dx
=(x-1+x+1)
dx=2xdx
(4)y=cos3x
dy=-sin3x
3
dx=
-3sin3xdx
(5)y=(2-3x^2)^3
dy=(2-3x^2)^3
=3(2-3x2)2(-6x)
dx=--18x(2-3x2)2
dx
(6)y=insin(2x-1)
dy=1/sin(2x-1)
cos(2x-1)
2
dx
=2/sin(2x-1)
cos(2x-1)
dx
求下列隐函数的导数yx‘：是对x求导吗
(1)x^3+6xy+5y^3=3
3x2+6y+6xy'+15y2y’=0
--------
提取y'化简
(2)y=x+(1/2)iny
y'
=1+(1/2)(1/y)
y'
提取y'化简