Differentiating $\tan\left(\frac{1}{ x^2 +1}\right)$ Differentiate: $\displaystyle \tan \left(\frac{1}{x^2 +1}\right)$
Do I use the quotient rule for this question? If so how do I start it of?

Answering this one too now, I'll write the steps straight away
$$\frac{d}{dx}\left(\tan \frac{1}{1+x^2} \right)=
\frac{d}{dy}\left.\left(\tan y \right)\right|_{y=\frac{1}{1+x^2}}
\cdot\frac{d}{dx}\left( \frac{1}{1+x^2} \right)$$
$$=\sec^2y|_{y=\frac{1}{1+x^2}} \cdot \left( - \frac{2x}{1+x^2} \right)$$
$$=\sec^2 \left( \frac{1}{1+x^2} \right) \cdot \left( - \frac{2x}{1+x^2} \right)$$
