Definition of Derivative

Let f(x) contains an open interval containing x_0 in its domain, the function is differentiable if the limit


L = \lim\limits_{\Delta x \to0} \dfrac{f(x_0+\Delta x )-f(x)}{\Delta x }


exist.

Binomial theorem

\begin{pmatrix} n \\ 0 \end{pmatrix}x^ny^0 + \begin{pmatrix} n \\ 1 \end{pmatrix}x^{n-1}y^1+ \begin{pmatrix} n \\ 2 \end{pmatrix}x^{n-2}y^2+\dots+ \begin{pmatrix} n \\ n-1 \end{pmatrix}x^1y^{n-1}+ \begin{pmatrix} n \\ n \end{pmatrix}x^0y^n