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#