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#.