Question

设x＝y²＋y，u＝（x²＋x）∧3/2，求dy/dx 为什么答案是1/3（2x＋1）（2y＋1

设x＝y²＋y，u＝（x²＋x）∧3/2，求dy/dx
为什么答案是1/3（2x＋1）（2y＋1）（√x²＋x）要详细步骤。

Answer 1

x = y² + y.........................................(1)
1 = 2yy' + y'...................................(2)
y' = dy/dx = 1/(1+2y) ..............(3)

追问

题目写错了，是求dy/du

追答

u＝（x²＋x）∧3/2...........................(4) 函数变换
u²/³ = x²+x.........................................(5) 两边对u求导数
(²/³)u^(²/³ -1) = 2xdx/du +dx/du = dx/du(1+2x)
dx/du = (2/3)/[(1+2x)u^(1/3)].........(6)
dy/du = dy/dx dx/du = (2/3)[(1+2y)(1+2x)u^(1/3)] ...........（7)
而：u^(1/3)=√(x²+x)...............(8)
dy/du = 2/[3(1+2x)(1+2y)√(x²+x)]...............(9)
与题中给的答案只差一个2倍！我算的找不出问题.