# The Power Rule - Calculus - 04 Jun 2018 at 02:06

## The Power Rule - Calculus

The Power Rule in Calculus is used when finding derivatives, and can be simplified to the following steps:

1. Multiply the term by the exponent (power)
2. Subtract 1 from the exponent

The result of taking the derivative of f(x) is often written as f'(x) (f prime of x).

To generalise:

d/dx x^n = nx^(n-1)

Some examples:

 f d/dx f' Notes f(x^3) x^3 = (3)x^(3-1) = 3x^2 3x^2 f(x^2) x^2 = (2)x^(2-1) = 2x^1 = 2x 2x f(x) x = x^1 = (1)x^(1-1) = x^0 = 1 1 x is the same as x^1 Any term raised to the power of 0 is always 1 f(x^0) x^0 = (0)x^(0-1) = 0^-1 = 0 0 f(x^-1) x^-1 = (-1)x^(-1-1) = -x^-2 -x^-2 or: -1/x^2 This can be written either way f(x^-2) x^-2 = (-2)x^(-2-1) = -2x^-3 -2x^-3 or: -2/x^3 This can be written either way f(x^-3) x^-3 = (-3)x^(-3-1) or: = -3x^-4 -3x^-4 or: -3/x^4 This can be written either way