The Power Rule | How to Find the Derivative of a Function with Exponentiation

Power Rule:d/dx [x^n] = ___________________

The power rule states that when you differentiate a function that is of the form f(x) = x^n, where n is a constant, you can find its derivative by multiplying the exponent (n) with the coefficient of the variable (x) and then subtracting 1 from the exponent

The power rule states that when you differentiate a function that is of the form f(x) = x^n, where n is a constant, you can find its derivative by multiplying the exponent (n) with the coefficient of the variable (x) and then subtracting 1 from the exponent.

In mathematical notation, the power rule can be expressed as:

d/dx [x^n] = n*x^(n-1)

Let’s break it down with an example:

If we have the function f(x) = x^3, applying the power rule will give us:

d/dx [x^3] = 3*x^(3-1) = 3*x^2

So the derivative of x^3 is 3x^2.

This rule is a fundamental rule in calculus and is widely used to differentiate polynomial functions and power functions. It allows us to find the instantaneous rate of change (slope) of these functions at any point.

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