Find the 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) : (ax+b)(cx+d)2
Let f(x)=(ax+b)(cx+d)2
Thus by Leibnitz product rule
f′(x)=(ax+b)ddx(cx+d)2+(cx+d)2ddx(ax+b)
=(ax+b)ddx(c2x2+2cdx+d2)+(cx+d)2ddx(ax+b)
=(ax+b)[ddx(c2x2)+ddx(2cdx)+ddxd2]+(cx+d)2[ddxax+ddxb]
=(ax+b)(2c2x+2cd)+(cx+d2)a
=2a(ax+b)(cx+d)+a(cx+d)2