Understanding the Power Rule | Differentiating Functions of the Form f(x) = x^n

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

The power rule is a basic rule in calculus that allows us to differentiate functions of the form f(x) = x^n, where n is a constant

The power rule is a basic rule in calculus that allows us to differentiate functions of the form f(x) = x^n, where n is a constant.

According to the power rule, the derivative of x raised to the power n (d/dx [x^n]) is equal to n times x raised to the power (n-1).

In mathematical notation, we can represent this as follows:

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

To illustrate this with an example, let’s say we have the function f(x) = x^3. We can find its derivative using the power rule:

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

Thus, the derivative of x^3 is 3x^2.

It is important to note that the power rule only applies when differentiating with respect to x. If the variable we are differentiating with respect to is different from x, we need to use a more general rule, known as the chain rule.

More Answers: