Question

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) : $(a{x}^2+\sin x)(p+q\cos x)$

Answer 1

Let $f\left(x\right)=(a{x}^2+\sin x)(p+q\cos x)$
Thus by product rule,
$f^{\prime }\left(x\right)=(a{x}^2+\sin x)\frac{d}{dx}(p+q\cos x)+(p+q\cos x)\frac{d}{dx}(a{x}^2+\sin x)$
$=(a{x}^2+\sin x)(-q\sin x)+(p+q\cos x)\frac{d}{dx}(a{x}^2+\sin x)$
$=-q\sin x(a{x}^2+\sin x)+(p+q\cos x)(2ax+\cos x)$