Question

What is the derivative of `x^3`?

Answer 1

`3x^2`

Explanation:

The derivative of `x^3` can be found using the power rule, which can be applied to polynomials of the form `ax^n`. When the coefficient of `x` is larger than one, the two numbers are multiplied together.

The power rule states:

`d/dx[ax^n]=nax^(n-1)` where `a,n` are constants

So for the derivative of `x^3`, since the coefficient is 1, then the number does not change. The coefficient is 3 because `1 times 3=3`, and the exponent is reduced by 1. Hence, `d/dx [x^3]=3x^2`.