Finding the derivative of a polynomial.

Take any polynomial, eg/ y=x³+¹/₂x²-3x+9. Then ^dy/_dx=3x,+x-3, in this case. This is because, when deriving in this sense, you take each term in x, multiply it by its index, and reduce that index by 1.

In a general sense, for y=(n₀)xⁿ+(n₁)x^n-1+...+(n_n-1)x^n-(n-1)+(n_n),             ^dy/_dx=(n)(n₀)x^n-1+(n-1)(n₁)x^n-2+...+(n-(n-1))(n_n-1). Multiply the x term by the power, reduce the power by one. This works for all powers, even non-integers.