Infinite differentiation

Whatever the power of $x$ might be, if the power is a positive integer, after a certain times of differentiation the output will be $0$ .

Notice that, after each differentiation power of x is becoming less by 1. In this case the 2015th derivative will have a constant multiplied by $x^{0}=1$ and the result will be a constant.

Now, what do we get when we differentiate a constant?

$\rightarrow$ Of course, $\color{#69047E} {\boxed{0}}$ .

For example, let's try this with $x^3$ :

$\frac{d} {dx} x^{3}=3x^{2}$ $\Rightarrow \frac{d} {dx} 3x^2= 3\times2x=6x$ $\Rightarrow \frac{d} {dx} 6x=6$ $\Rightarrow \frac{d} {dx}6=\color{#69047E} {\boxed{0}}$

Consider:- $\frac{d}{dx}x^{2015}$

This gives $2015x^{2014}$

Continuing this till some integer $a$ which ultimately gives 0