The power rule can be applied to expressions containing a
variable with a constant exponent, such as x

^{2}, x^{-4}, x^{-1/3}, and x^{2/5}. It also applies to variables having complex number exponents, such as x^{i}and x^{(2 + 3i)}.
The power rule does not apply to expressions in which a constant
has a variable exponent, such as e

^{x}or 10^{x}. It does not apply to variables having variable exponents as well, such as x^{x}.
The power rule can be represented by the following formula:

To differentiate it, the power rule is to be applied, because there is a variable with a constant exponent. The variable is x, and exponent is 5.

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

…where x is a variable and n is a number. In words, the power rule says that if a variable has an exponent of a number, say n, then its derivative is given by n times the variable with an exponent of one less than n.

The following procedure sums up how power rule is applied,

- Take the exponent on the variable, and place it before the variable
- Reduce the exponent on the variable by 1 and let this become the new exponent on the variable

The exponent on the variable can be a negative or positive number, zero, a fraction, a decimal number or a complex number.

For example, consider the following function,

`f(x) = x^5`

- Take the exponent 5 and place it before the variable
- Take the exponent 5, reduce it by 1 to get 4, and let this become the new exponent on the variable

`f'(x) = 5x^4`

Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the "equals" sign in (5)(5)(5) = 53.

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