<s>[INST] Using the Chain Rule Find $dy/dx$. $y=x/\sqrt{x^2+1}$. I started with the quotient rule and got $y'=(x^2+1)^{1/2}-x^2(x^2+1)^{1/2 }$all over $((x^2+1)^{1/2})^2$. I can not find my mistake. 
 [/INST] Another way: 
Product rule
\begin{align*}
y' = [x(x^2+1)^\frac{-1}{2}]' &= x\frac{-1}{2}(x^2+1)^\frac{-3}{2}(2x) + 1(x^2+1)^\frac{-1}{2}\\
&= -x^2(x^2+1)^\frac{-3}{2} + (x^2+1)^\frac{-1}{2}\\
&= \frac{-x^2}{(x^2+1)^{\frac{3}{2}}}+ \frac{1}{(x^2+1)^\frac{1}{2}}\\
&= \frac{-x^2}{(x^2+1)^{\frac{3}{2}}}+ \frac{1}{(x^2+1)^\frac{1}{2}}\frac{x^2+1}{x^2+1}\\
&= \frac{1}{(x^2+1)^\frac{3}{2}}
\end{align*}
</s>