Find derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): `(a x + b) (c x + d)^2`

Explanation

Let `f(x)=(ax+b)(cx+d)^2`

Thus by Leibnitz product rule

`f′(x)=(ax+b)d/(dx)(cx+d)^2+(cx+d)^2d/(dx)(ax+b)`

=`(ax+b)d/(dx)(c^2x^2+2cdx+d^2)+(cx+d)^2 d/(dx) (ax+b)`

`= (ax+b)[d/(dx)(c^2x^2)+d/(dx)(2cdx)+d/(dx)d^2]+(cx+d)^2[d/(dx)ax+d/(dx)b]`

=`(ax+b)(2c^2x+2cd)+(cx+d^2)a`

=`2a(ax+b)(cx+d)+a(cx+d)^2`