Question

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

Answer 1

`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`

Answer 2

`(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`