Question

Find the derivative of :-
(Ax + B)^m(Cx + D)^n​

Answer 1

Step-by-step explanation:

f(x)=(ax+b) n (cx+d) n

f(x)=(ax+b) n (cx+d) nu=(ax+b) n ⇒u ′ =an(ax+b) n−1

f(x)=(ax+b) n (cx+d) nu=(ax+b) n ⇒u ′ =an(ax+b) n−1v=(cx+d) n ⇒v ′ =cn(cx+d) n−1

f(x)=(ax+b) n (cx+d) nu=(ax+b) n ⇒u ′ =an(ax+b) n−1v=(cx+d) n ⇒v ′ =cn(cx+d) n−1f ′ (x)=(uv) ′

f(x)=(ax+b) n (cx+d) nu=(ax+b) n ⇒u ′ =an(ax+b) n−1v=(cx+d) n ⇒v ′ =cn(cx+d) n−1f ′ (x)=(uv) ′=uv ′ +vu ′

f(x)=(ax+b) n (cx+d) nu=(ax+b) n ⇒u ′ =an(ax+b) n−1v=(cx+d) n ⇒v ′ =cn(cx+d) n−1f ′ (x)=(uv) ′=uv ′ +vu ′=(ax+b) n cn(cx+b) n−1 +(cx+b) n an(ax+b) n−1