Mastering the Power Rule | A Fundamental Guide to Calculus Derivatives of Functions Raised to a Power

Power Rule

The power rule is a fundamental rule in calculus that allows us to find the derivative of a function that is raised to a power

The power rule is a fundamental rule in calculus that allows us to find the derivative of a function that is raised to a power. It is used when we differentiate functions of the form f(x) = x^n, where n is any real number.

The power rule states that if we have a function f(x) = x^n, where n is a constant, then the derivative of f(x), denoted as f'(x), is given by:

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

In simpler terms, the power rule tells us that when we differentiate a function that is raised to a power, we bring down the power as the coefficient and reduce the power by 1.

For example, let’s say we want to find the derivative of the function f(x) = x^3. Using the power rule, we bring down the power 3 as the coefficient and reduce the power by 1 to get:

f'(x) = 3 * x^(3-1) = 3 * x^2

So, the derivative of f(x) = x^3 is f'(x) = 3x^2.

The power rule is extremely useful in calculus, as it allows us to find the derivatives of polynomial functions with ease. It is often used in combination with other rules and techniques to find the derivatives of more complex functions.

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