Homework 1 collaboration area

Here is an example of how to input math:

$ \int_0^\pi\sin x\,dx = \left[ -\cos x\right]_0^\pi = -(-1)-(-1)=2 $

How do you compute the derivative of

$ \frac{x^2+1}{3x^4-7}? $

just for testing:

$ \int_a^bf'(x)\,\mathrm{d}x=f(b)-f(a) $

$ \Gamma(z)=\int_0^\infty t^{z-1}\mathrm{e}^{-t}\,\mathrm{d}t $

$ f^{(n)}(z)=\dfrac{n!}{2\pi\mathrm{i}}\oint_\gamma\dfrac{f(t)}{(t-z)^{n+1}}\,\mathrm{d}t $