Find the derivative of the following function ( it is to be understood that a, b, c and d are fixed non-zero constants and m and n are integers ) :-
[tex]\sf \: (ax + b) ^{n} ( {cx + d})^{n} [/tex]
[tex]\sf \: (ax + b) ^{n} ( {cx + d})^{n} [/tex]
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⭐Answer⭐
Let f(x) = (ax + b) (cx + d)^2
Thus by leibnitz product rule.
f'(x) = (ax + b) d/dx (cx + d)^2 + (cx + d)^2 d/dx (ax + b).
(ax + b) d/dx (c^2x^2 + 2 cdx + d^2) + (cx+d)^2 d/dx (ax + b)
(ax + b) [d/dx (c^2 x^2) + d/dx (2cdx) + d/dx d^2]
(cx + d)^2 [d/dx ax + d/dx b]
(ax + b) (2c^2 x + 2cd) + (cx + d^2)a
2a(ax + b) (cx + d) + a(cx + d)^2
Hope it helps❤