下y=x的3/4次方的导数和y=x的5/2次方比x的1/3次方的导数

楼上都解错了一道题。

y = x^(¾)
dy/dx = ¾ x^(-¼)

y = x^(5/2)/x^(1/3)=x^(13/6)
dy/dx = (13/6)x^(7/6)

公式：(x^a)'=ax^(a-1).........(a-1)是指数

y’=(x^3/4)'
=(3/4)x^(-1/4)..........(-1/4)是指数

y'=[x^(5/2)/x^(1/3)]'
=[x^(4/3)]'
=(4/3)x^(1/3)..........(1/3)是指数

公式：(x^a)'=ax^(a-1).........(a-1)是指数

y’=(x^3/4)'
=(3/4)x^(-1/4)..........(-1/4)是指数

y'=[x^(5/2)/x^(1/3)]'
=[x^(4/3)]'
=(4/3)x^(1/3)..........(1/3)是绝对正确哦

y=x^(3/4)的导数
y'=(3/4)x^(3/4-1)=(3/4)x^(-1/4)
y=x^(5/2)/x^(1/3)的导数
y'=[(x^(5/2))'*x^(1/3)-x^(5/2)*(x^(1/3)')]/[x^(1/3)]^2
=[(5/2)*x^(3/2)*x^(1/3)-(1/3)*x^(5/2)*x^(-2/3)]/x^(2/3)
=[(5/2)*x^(11/6)-(1/3)*x^(11/6)]/x^(2/3)
=(13/6)*x^(11/6)/x^(2/3)
=(13/6)x^(7/6)