Question

Find the derivative of $y=(x+1)(x+2{)}^2$

Answer 1

$y=(x+1)(x+2{)}^2$

$\frac{dy}{dx}=(x+1)\frac{d}{dx}(x+2{)}^2+(x+2{)}^2\frac{d}{dx}(x+1)$ [Apply product Rule of differentiable]

$\left[\frac{d}{dx}f\right(x)\cdot g(x)=\frac{d}{dx}f(x).q(x)+\frac{d}{dx}g(x\left)\right]$

$=(x+1)\cdot 2(x+2)+(x+2{)}^2\cdot 1$

$=(x+2)\left[2\right(x+1)+x+2]$

$=(x+2)[2x+2+x+2]$

$=(x+2)[3x+4]$

$=(x+2)(3x+4)$.