导数运算法则

Question 1

[u(x)+/-v(x)]’=?

Answer 1

u’(x)+/-v’(x)

Question 2

[u(x)v(x)]’=?

Answer 2

u’(x)v(x)+u(x)v’(x)

Question 3

[u(x)/v(x)]’=?

Answer 3

[u’(x)v(x)-u(x)v’(x)]/v(x)^2 (v(x)|=0)

Question 4

反函数：

dy/dx=?

Answer 4

1/(dx/dy)

Question 5

复合函数：

dy/dx=?

Answer 5

(dy/du)/(du/dx)

Question 6

u->0,u的等价无穷小？

Answer 6

sin(u), arcsin(x), tan(x), arctan(u),

ln(1+u), e^u-1

Question 7

1-cos(x)的等价无穷小？

Answer 7

u^2/2

Question 8

(1+u)^0.5-1的等价无穷小？

Answer 8

u/2

Question 9

(1+x)^(1/n)-1的等价无穷小？

Answer 9

x/n