Question

求函数fx=(x-2)(x+2)^2/3的导数

Answer 1

y=(x-2)*(x+2)^(2/3)

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

=[(x+2)^(2/3)+(2/3)(x-2)(x+2)^(-1/3)]

=(x+2)^(-1/3)[(x+2)+(2/3)(x-2)]

=(1/3)(x+2)^(-1/3)(x+2+2x-4)

=(1/3)(x+2)^(-1/3)(3x-2).