Reviewing the rules of calculus, you know that

$\frac{d}{dx}(a f(x) + b g(x)) = a \frac{d}{dx}f(x) + b \frac{d}{dx}g(x)$

and

$\frac{d}{dx}(f(x)g(x)) = \left( \frac{d}{dx}f(x) \right) g(x) + f(x) \left(\frac{d}{dx}g(x) \right)$

From these two rules, or from first principles, you can determine that

$\frac{d}{dx}\left(a x^n\right) = na x^{n - 1}$.

Suppose you have a table, the entries of which are labelled $0$ through $n$ where $n$ is the degree of a polynomial, and the entry indexed by $k$ is the coefficient of $x^k$.

For example, suppose we had the table

0	1	2
-0.807	-1.32	1.99

This table represents the polynomial $1.99x^2 - 1.32x - 0.807$.

Describe an algorithm that calculates the derivative of such a polynomial, putting the derivative into a new table with $n$ entries labelled $0$ through $n - 1$.