Question

Find the derivative of the following function (it is to be understood that a, b, c, d are fixed non-zero constants):
f(x)= $(ax+b)(cx+d{)}^2$

Answer 1

$(ax+b)(cx+d{)}^2$

Here f(x)= $(ax+b)(cx+d{)}^2$

$\therefore f^{\prime }\left(x\right)=\frac{d}{dx}\left[\right(ax+b\left)\right(cx+d{)}^2]$

$=(ax+b)\frac{d}{dx}(cx+d{)}^2+(cx+d{)}^2.\frac{d}{dx}(ax+b)$

$=(ax+b)\times 2(cx+d)\times c+(cx+d{)}^2\times a$

$=2c(ax+b)(cx+d)+a(cx+d{)}^2$