Power Rule Calculator
Enter a monomial a*x^n (e.g., 3x^2) to compute its derivative via the power rule.
Step-by-step method
- Set up the problem.
- Identify the coefficient a and exponent n.
- Apply the power rule: d/dx(a·x^n) = a·n·x^(n−1).
- Simplify if needed.
Formula:
| d |
| dx |
Example 1: f(x) = 3x^2
Step 1 - Set up the problem.
In this problem: We will differentiate f(x) with respect to x.
Step 2 - Identify a and n.
In this problem: Match your monomial to a·x^n.
Step 3 - Apply the power rule.
In this problem: Use a·n·x^(n−1).
| d |
| dx |
Final answer: f'(x) = 6x
Example 2: f(x) = (1/2)x^3
Step 1 - Set up the problem.
In this problem: We will differentiate f(x) with respect to x.
| 1 |
| 2 |
Step 2 - Identify a and n.
In this problem: Match your monomial to a·x^n.
| 1 |
| 2 |
Step 3 - Apply the power rule.
In this problem: Use a·n·x^(n−1).
| d |
| dx |
| 1 |
| 2 |
| 1 |
| 2 |
| 3 |
| 2 |
Final answer: f'(x) = 3x^2/2
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