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Calculator form
Enter coefficients from highest degree to constant. Example: 1,3,2 means x2 + 3x + 2.
Formula used
dn/dxn [f(x)g(x)] = Σk=0n C(n,k) · f(k)(x) · g(n-k)(x)
This page accepts two polynomials, forms their product, and evaluates the nth derivative using the theorem sum.
For verification, it also differentiates the expanded product directly and confirms both results match.
How to use this calculator
- Enter polynomial coefficients for f(x) and g(x) from highest power to constant.
- Choose the derivative order n.
- Enter the x-value where you want the derivative evaluated.
- Set graph start and graph end values for visual comparison.
- Press Calculate derivative to show the result above the form.
- Review the theorem expansion table, graph, and verification message.
- Use the CSV or PDF buttons to export the report.
Example data table
Sample input and output for a quick check.
| f(x) coefficients | g(x) coefficients | n | x | Product | Derivative result | Value at x |
|---|---|---|---|---|---|---|
| 1, 3, 2 | 2, 1 | 2 | 2 | 2x3 + 7x2 + 7x + 2 | 12x + 14 | 38 |
FAQs
1. What does this calculator compute?
It computes the nth derivative of a product of two polynomials using Leibnitz theorem, then evaluates that derivative at a chosen x-value and plots the result.
2. How should I enter coefficients?
Enter numbers from highest degree to constant, separated by commas. For example, 3,0,-2,5 means 3x3 - 2x + 5.
3. Why does the result become zero sometimes?
If the derivative order exceeds the degree of the product polynomial, the derivative eventually becomes zero. That is expected for polynomial inputs.
4. What is C(n,k) in the theorem table?
C(n,k) is the binomial coefficient. It weights each paired derivative term in the theorem sum and determines how strongly each split contributes.
5. Does this calculator support non-polynomial functions?
This version focuses on polynomial inputs so the derivatives, symbolic forms, and graphs stay exact, clear, and fast to verify.
6. Why is there a verification message?
The page checks the theorem result against the derivative of the expanded product. Matching outputs help confirm the entered data and computation are consistent.
7. What do the download buttons include?
The CSV and PDF exports include the input summary, derivative result, evaluation value, verification status, and the theorem term breakdown table.
8. Can I use decimal coefficients?
Yes. Decimal and negative coefficients are accepted, provided they are numeric and separated with commas in the correct order.