作业帮求y=(x+1)(x+2)(x+3)的导数
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求y=(x+1)(x+2)(x+3)的导数
求y=(x+1)(x+2)(x+3)的导数
求y=(x+1)(x+2)(x+3)的导数
y' = (x+1)'(x+2)(x+3)+(x+1)(x+2)'(x+3)+(x+1)(x+2)(x+3)'
=(x+2)(x+3)+(x+1)(x+3)+(x+1)(x+2)
=3x²+12x+11
对数求导法。
lny=ln(x+1)+ln(x+2)+ln(x+3)
两边对x求导
y'/y=1/(x+1)+1/(x+2)+1/(x+3)
y'=(x+2)(x+3)+(x+1)(x+3)+(x+1)(x+2)
y=(x+1)(x+2)(x+3)=(x^2+3x+2)(x+3)=x^3+6x^2+11x+6
所以导数为3x^2+12x+11
y=x³+6x²+11x+6
y′=3x²+12x+11
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