## Power Rule

### The power rule is a fundamental rule in calculus that is used to differentiate functions of the form f(x) = x^n, where n is a constant exponent

The power rule is a fundamental rule in calculus that is used to differentiate functions of the form f(x) = x^n, where n is a constant exponent. It states that the derivative of such a function is given by:

f'(x) = n * x^(n-1)

In other words, when differentiating a function with a constant exponent, you can bring down the exponent as a coefficient in front of the function, and then subtract 1 from the exponent.

Here are a few examples to illustrate the power rule:

1. If f(x) = x^2, then applying the power rule gives f'(x) = 2 * x^(2-1) = 2x.

2. If g(x) = x^4, then applying the power rule gives g'(x) = 4 * x^(4-1) = 4x^3.

The power rule can be extended to handle more complex functions that involve a combination of basic power functions and constants. For instance, if we have a function h(x) = 3x^5, we can apply the power rule as follows:

h'(x) = 5 * 3 * x^(5-1) = 15 * x^4

It is important to note that the power rule is only applicable to functions where the base is a variable raised to a constant exponent. It does not apply to functions where the exponent itself is a variable or includes other terms. In such cases, more advanced derivative rules, like the chain rule or product rule, would be needed.

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