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How to Take the Derivative of x^2: Steps & Tutorial

Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Getting the basics right is important! In this lesson, you will learn how to find the derivative of the relatively simple term x^2. You'll see the underlying method that lets you solve the derivatives of expressions of any power and you'll also learn how to verify that your answer is correct.

Method

In order to find the derivative of x^2 we need to use something called the power rule of differentiation. This rule states that the following is true.


power rule for derivatives


Here x is a variable, and n is any value in that variable's exponent.

Steps

Step 1, identify what our value of n is for using the power rule. In the case of x^2, n equals 2.


solving the derivative part 1


Step 2, simplify the exponent of your solution.


solving the derivative solution


Solution

In this lesson we found that the derivative of x^2 is equal to 2x.

Checking Your Work

In order to check our work we can take the indefinite integral, a.k.a. the antiderivative, of 2x. While we only had to use one rule to differentiate x^2 in our previous section, taking the indefinite integral of 2x will actually take two different rules.

The first rule we need will tell us how to integrate a function (f(x)), multiplied by a constant (c).


constant rule for integration


In the case of 2x; our function is x, and our constant is 2.


part 1 of solving our integral


Now we can get to using our second rule. To solve the indefinite integral of x we need to use the power rule of integration.


power rule of integration


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