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# 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 ) $(ax+b)(cx+d)^2$

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## 1 Answer

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Let $f(x) = (ax+b)(cx+d)^2$
By Leibnitz product rule
$f'(x) = (ax+b)\large\frac{d}{dx}$$(cx+d)^2 + (cx+d)^2\large\frac{d}{dx}$$(ax+b)$
$= (ax+b) \large\frac{d}{dx}$$(c^2x^2+2cdx+d^2)+(cx+d)^2\large\frac{d}{dx}$$(ax+b)$
$(ax+b) \bigg[ \large\frac{d}{dx}$$(c^2x^2)+ \large\frac{d}{dx}$$(2cdx)+\large\frac{d}{dx}$$d^2 \bigg]$$+ (cx+d)^2 \bigg[ \large\frac{d}{dx}$$ax+ \large\frac{d}{dx}$$b \bigg]$
$= (ax+b) (2c^2x+2cd)+(cx+d^2)a$
$= 2c(ax+b)(cx+d)+a(cx+d^2)$
answered Apr 12, 2014

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