Derivative Calculator
Compute the derivative of ax^n using the power rule.
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Introduction
Derivative Calculator — Compute the derivative of ax^n using the power rule. Enter Coefficient a, Exponent n, x to get an instant, accurate result.
Formula
Power rule: d/dx[a×xⁿ] = a×n×x^(n−1), evaluated exactly (not numerically approximated) at the given x.
Step-by-step
- Enter the Coefficient a.
- Enter the Exponent n.
- Enter the x.
- Click Calculate to see your result instantly.
Real-world example
Example: With Coefficient a = 2, Exponent n = 3, x = 2, the Derivative Calculator gives Coefficient: 6, Exponent: 2, Value At X: 24.
Frequently Asked Questions
Is this an exact or approximate derivative?
Exact — it applies the power rule symbolically, then evaluates the resulting expression at your x value.
What if n = 0?
The term a×x⁰ is just the constant a, so its derivative is 0.
What inputs does the Derivative Calculator need?
You'll need to provide: Coefficient a, Exponent n, x. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Derivative Calculator?
The Derivative Calculator applies the formula exactly as calculated — Power rule: d/dx[a×xⁿ] = a×n×x^(n−1), evaluated exactly (not numerically approximated) at the given x. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Derivative Calculator free to use?
Yes, the Derivative Calculator is completely free, requires no signup, and runs instantly in your browser.
About the Derivative Calculator
The Derivative Calculator uses a real, verifiable formula — Power rule: d/dx[a×xⁿ] = a×n×x^(n−1), evaluated exactly (not numerically approximated) at the given x. — so results are accurate every time, not an approximation.