f(x)=(x-1)^2(x+1)^3 求导

来源：学生作业帮助网编辑：作业帮时间：2024/05/10 09:11:55

f(x)=(x-1)^2(x+1)^3 求导
f(x)=(x-1)^2(x+1)^3 求导

f(x)=(x-1)^2(x+1)^3 求导
=(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

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)]

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

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

已知f(x)满足2f(x)+f(1/x)=3x,求f(x) F(X)满足F(x)+2f(x分之1)=3X,求f(x) 已知f(x)满足2f(x)+f(1/x)=3x,求f(x)? 已知f(x)满足2f(x)+f(-x)=-3x+1,求f(x) 已知f(x)满足f(x)+2f(1/x)=3x,求f(x) , f(x+1)+f(x-1)=4x^3-2x求f(x) 已知f(x+1/x-1)=3f(x)-2x,求f(x) 已知函数f(x)=x^3+x^2-2x-x,f(1)f(2) 设f(x)={3x-1,x=0,求f(-x),f(x-2). 已知f(x)+2f(1/x)=x+2/x+3,求f(x) f(x)=5x+3 f(x)=5x f(x)=x+2x+1 f(x)=5x+3 f(x)=5x f(x)=x+2x+1 f(x-1)=x^2-2x+3(x f(x)=(x-1)(x-2).(x-3)求导 f(x)+2f(1/x)=3x f(1+x)+2f(1-x)=3x^2 求f(x)f(1+x)+2f(1-x)=3x^2求f(x) F(x)=3x^2+2x-1 求F(x+△x)-f(x)/ △x f(x)满足f(-x)+2f(x)=x+3,则f(1)等于 (1) 已知f(x+1)=x*2+x,求f(x).(2)已知f(x-1/x)=(x+1/x)*2,求f(x) (3)已知f[f(x)]=2x)-1,求一次函数f(x)