Question

Find 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) : $(x^2+1)\cos x$

Answer 1

Let $f\left(x\right)=(x^2+1)\cos x$
Thus by product rule
$f^{\prime }\left(x\right)=(x^2+1)\frac{d}{dx}\left(\cos x\right)+\cos x\frac{d}{dx}(x^2+1)$
$=(x^2+1)(-\sin x)+\cos x\left(2x\right)$
$=-x^2\sin x-\sin x+2x\cos x$