Y=(x+1)(x+2)(x+3) Find dy/dx?

2 Answers
Jan 9, 2018

dy/dx=3x^2+12x+11

Explanation:

"expanding the factors gives"

y=x^3+6x^2+11x+6

"differentiate each term using the "color(blue)"power rule"

•color(white)(x)d/dx(ax^n)=nax^(n-1)

rArrdy/dx=3x^2+12x+11

Jan 9, 2018

(dy)/dx=3x^2+10x+11

Explanation:

Using the product rule:

d/(dx)(utimesvtimesw)=(du)/dxtimesvtimesw+utimes(dv)/dxtimesw+utimesvtimes(dw)/dx

We get:

(dy)/dx=(d(x+1))/dxtimes(x+2)times(x+3)+(x+1)times(d(x+2))/dxtimes(x+3)+(x+1)times(x+2)times(d(x+3))/dx

Using the rule: (d(ax+b))/dx=a

(dy)/dx=1times(x+2)times(x+3)+(x+1)times1times(x+3)+(x+1)times(x+2)times1

Simplifying:

(dy)/dx=x^2+5x+6+x^2+3x+3+x^2+2x+2

(dy)/dx=3x^2+10x+11