Question

高数函数二价导数习题

(1)y=2x^3-9x^2+12x-3

(2)y=x(1+立方√x^2)

(3)y=x+1/x

(4)f(x)=(x-4)^5/3，求f''(0)
答案是
1.12x-18
2.(10/9)x^(-1/3)
3.2/x^3
4.-5/9*立方根2

求过程

Answer 1

(1)y=2x^3-9x^2+12x-3
y'=6x^2-18x+12
y''=12x-18

(2)y=x(1+立方√x^2)
y'=1+立方√x^2+x(2/3*x^(-1/3))
y''=4/3*x^(-1/3)-2/9*x^(-4/3)

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

(4)f(x)=(x-4)^5/3
f'(x)=5/3(x-4)^2/3
f''(x)=10/9(x-4)^(-1/3)
f''(0)= 10/9(-4)^(-1/3)