Question

y=(x+3)^2(x-2)^3求微分

y=(x+3)^2(x-2)^3求微分

Answer 1

y=(x+3)²×(x-2)³
y'=2(x+3)×(x-2)³+3(x+3)²(x-2)²
=(x+3)(x-2)[2(x-2)²+3(x+3)(x-2)]
∴dy/dx=(x²+x-6)(5x²-5x-10)

Answer 2

y = (x+3)^2(x-2)^3
dy = (2(x+3)(x-2)^3)dx + (3(x-2)^2(x+3)^2)dx
= (x+3)(x-2)^2[2(x-2) + 3(x+3)]dx
= 5(x+3)(x+1)(x-2)^2dx