Question

求第四题的步骤啊兄弟们，怎么算都算不对

Answer 1

y=3+x-x^(-1/3)
y=3
x-x^(-1/3) =0
x^3 -1 =0
x=1
dy/dx = 1 +(1/3)x^(-4/3)
1/dy/dx | x=1
= 1/[ 1 +1/3]
=3/4
x=φ(y) 在 y=3 处的导数 = 3/4

Answer 2

4.解：记 f(x)＝3+x-1/(³√x) (x>0)，则
f'(x)＝1+1/[3(³√x⁴)]＞0，f(x)单增，
且易见 f(1)＝3，f'(1)＝4/3，
所以，y=f(x)的反函数x=φ(y)在y=3处的导数为 φ'(3)＝1/f'(1)＝3/4 .