求y=(x+1)(x+2)(x+3)的导数?(ps;在这题中`是先算乘除还是加减?)
问题描述:
求y=(x+1)(x+2)(x+3)的导数?(ps;在这题中`是先算乘除还是加减?)
答
y==(x+1)(x+2)(x+3)
y'=(x+1)'(x+2)(x+3)+(x+1)((x+2)(x+3))'
=(x+2)(x+3) +(x+1)((x+2)'(x+3)+(x+2)(x+3)')
=x^2+5x+6 +(x+1)((x+3)+(x+2)
=x^2+5x+6 +(x+1)(2x+5)
=x^2+5x+6 +2x^2+5x+2x+5
=3x^2+12x+11