高二数学求f（x）=x的三次方减2除以2乘（x-1）的平方这条函数的导函数怎么算要详细过程

Question

高二数学求f（x）=x的三次方减2除以2乘（x-1）的平方这条函数的导函数怎么算要详细过程

Answer 1

f(x)=(x^3-2)/[2(x-1)^2]
f'(x)=[ (3x^2)(x-1)^2-(x^3-2)*2(x-1)]/[2(x-1)^4]
=[(3x^2(x-1)-2(x^3-2)/[2(x-1)^3]
=[3x^3-3x^2-2x^3+4]/[2(x-1)^3]
=(x^3-3x^2+4)/[2(x-1)^3]