Question

函数y=(x-1)(x-2)(x-3)(x-4)，求导，顺便给个过程，谢谢！

Answer 1

楼上的那些方法不实际！lny=ln(x-1)+ln(x-2)+ln(x-3)+ln(x-4)，左右求导，就容易得到y'

Answer 2

y'=[(x-1)(x-2)(x-3)(x-4)]'
=(x-1)'(x-2)(x-3)(x-4)+(x-1)(x-2)'(x-3)(x-4)+(x-1)(x-2)(x-3)'(x-4)+(x-1)(x-2)(x-3)(x-4)'
=(x-2)(x-3)(x-4)+(x-1)(x-3)(x-4)+(x-1)(x-2)(x-4)+(x-1)(x-2)(x-3)

Answer 3

y=(x-1)(x-2)(x-3)(x-4)
lny=ln(x-1)(x-2)(x-3)(x-4)
2边对X求导
1/y^y’=1/（x-1）+1/（x-2）+.....
y‘=（x-2）^（X-3）^（X-4）+(X-1)^(X-3)^(X-4)+(X-1)^(X-2)^(X-4)+(X-1)^(X-2)^(X-3)

Answer 4

展开：
y=(x-1)(x-2)(x-3)(x-4)=x^4 - 10x^3 + 35x^2 - 50x + 24

求导得：dy/dx = 4x^3 - 30x^2 + 70x -50