Find the derivative of function (a x^2 + x)(p + q ; x) (it is to … - Vidyadip

Question

Find the derivative of function $(a{x^2} + \sin x)(p + q\;\cos x)$ (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).

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Answer

Here $f(x) = (ax^2 + sinx) (p + q cosx)$
$\therefore \;f'(x) = \frac{d}{{dx}}[(a{x^2} + \sin x)(p + q\cos x)]$
$= (a{x^2} + \sin x)\frac{d}{{dx}}(p + q\cos x) + (p + q\cos x)\frac{d}{{dx}}(a{x^2} + \sin x)$
$=\left(a x^2+\sin x\right)(-q \sin x)+(p+q \cos x)(2 a x+\cos x)$
$=-q \sin x\left(a x^2+\sin x\right)+(p+q \cos x)(2 a x+\cos x)$

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