Power Rule Calculator

This Power Rule Calculator helps you differentiate powers of x. The power rule is used when a variable is raised to a constant exponent, and it is one of the main rules needed before solving larger derivative problems. The calculator shows the setup, formula, substitution, solving work, and final answer.

Step-by-step method

1. Set up the problem.
2. Write the power rule formula.
3. Substitute the given power into the formula.
4. Solve and simplify.

Formula: This is the power rule formula.

Example 1: Take the problem x^2.

Step 1 - Set up the problem.

In this problem: We are given x^2. This is a power of x, so the exponent is n = 2.

Step 2 - Write the power rule formula.

In this problem: The power rule says to move the exponent to the front, then subtract 1 from the exponent.

Step 3 - Substitute the given power into the formula.

In this problem: Here, n = 2. Substitute this exponent into the power rule, but do not simplify yet.

Step 4 - Solve and simplify.

In this problem: Now subtract 1 from the exponent and simplify. This gives 2x.

Final answer: The final answer is 2x.

Example 2: Take the problem x^5.

Step 1 - Set up the problem.

In this problem: We are given x^5. This is a power of x, so the exponent is n = 5.

Step 2 - Write the power rule formula.

In this problem: The power rule says to move the exponent to the front, then subtract 1 from the exponent.

Step 3 - Substitute the given power into the formula.

In this problem: Here, n = 5. Substitute this exponent into the power rule, but do not simplify yet.

Step 4 - Solve and simplify.

In this problem: Now subtract 1 from the exponent and simplify. This gives 5x^4.

Final answer: The final answer is 5x^4.