Question

what is the derivative of \[\frac{ xsinx }{ x ^{2}+1 }\] in it's most simplified form

Answer 1

please help i got a really long answer and I need to find the second derivative as well so I figured there must be a simplified form but I'm struggling to get it

Answer 2

\[f(x)=\frac{x\sin x}{x^2+1}\\
\begin{align*}f'(x)&=\frac{(x^2+1)(\sin x+x\cos x)-(x\sin x)(2x)}{(x^2+1)^2}\\
&=\frac{(x^3+x)\cos x+(1-x^2)\sin x }{(x^2+1)^2}\end{align*}\]

Answer 3

thanks a bunch