Polynomial Derivative and Tangent Calculator
Differentiate a polynomial of degree up to six, evaluate its slope at a point and find the tangent line. Enter coefficients and follow each power-rule term.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Multiply each coefficient by its power and lower that power by one. The derivative of a constant is zero. Evaluate the original polynomial and its derivative at the entered x, then form y=f′(x₀)(x−x₀)+f(x₀).
d(axⁿ)/dx=na xⁿ⁻¹; tangent slope m=f′(x₀); tangent y=mx+[f(x₀)−mx₀]
Worked example
Coefficients 1,0,−3,2 represent f(x)=x³−3x+2. The derivative is 3x²−3. At x=2, f(2)=4 and f′(2)=9, so the tangent line is y=9x−14.
Assumptions and input details
Enter 1–7 coefficients in descending powers, including zeros for missing powers. Whole numbers, decimals with up to six places and fractions such as 1/2 are supported; magnitudes are limited to 1e6 and reduced input denominators to 1e6. The point uses the same input format and bound. Graph half-width must be positive and at most 100. This differentiates one explicit polynomial, not arbitrary expressions, trigonometric functions or piecewise functions. The exact fraction calculation is separate from the rounded graph.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Derivative coefficients, the chosen point, slope and tangent intercept use exact fraction arithmetic. Decimal approximations and the graph are rounded.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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