Question

求x-3的1╱2次方分之x的微积分

Answer 1

y=x/(x-3)^(1/2)

方法1

y'={x'(x-3)^(1/2)-x*[(x-3)^1/2]'}/(x-3)

y'=[(x-3)^1/2-x*1/2*(x-3)^(-1/2)]/(x-3)

y'=[x-3-x/2 * 1]/(x-3)^(3/2)

y'=(x-6)/[2(x-3)^(3/2)]

方法2:

y^2=x^2/(x-3)

两边求导：

2y*y'=(2x(x-3)-x^2)/(x-3)^2

2y'*x/(x-3)^(1/2)=(2x(x-3)-x^2)/(x-3)^2

2y'=(2(x-3)-x)/(x-3)^(3/2)

y'=(x-6)/[2(x-3)^(3/2)]