Question

f(x)=(x-1)^2(x+1)^3 求导

跪求过程~~~~~~~~~~~~~~~~~~~~

Answer 1

两边求对数得：

lnf(x) = ln(x-1)^2(x+1)^3
=2ln(x-1)+3ln(x+1)

两边求导：

f'(x)/f(x) = 1/x-1 + 3/x+1

f'(x) = (1/(x-1)+3/(x+1))f(x)

对于多项乘积的求导大多先求对数再求导比较方便

Answer 2

f(x)=(x-1)^2(x+1)^3
=[(x-1)(x+1)]^2(x+1)
=(x^2-1)^2(x+1)
=(x^4-2x^2+1)(x+1)
=x^5+x^4-2x^3-2x^2+x+1

f'(x)=5x^4+4x^3-6x^2-4x+1

Answer 3

f'(x)=2(x-1)(x+1)^3+(x-1)^2 *3(x+1)^2
=(x-1)(x+1)[2(x+1)^2+3(x-1)(x+1)]

Answer 4

=(x-1)^2*(x+1)^2*(x+1)
(x^2-1)^2*(x+1)
(x^4 - 2x^2+1)*(x+1)
x^5-2x^3+x+x^4 - 2x^2+1
求导得 5x^4+4x^3-6x^2-4x+1