doomath Calculator
Derivative & Tangent Line Calculator
Find polynomial first & second derivatives, evaluate slope f'(x₀), construct tangent line equations, and locate inflection points with full KaTeX steps.
InputsChange a value to recalculate instantly
ResultUpdates as you type
FORMULA & STEPSDerivative & Tangent Line Calculator — Mathematical Derivation & Steps
3 StepsSequential Calculation Breakdown
1
Differentiate term by term
Apply the power rule to each polynomial term.
2
Evaluate slope
The derivative at x₀ is the tangent slope.
3
Build tangent
Use point-slope form through (x₀, f(x₀)).
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Derivative & Tangent Line Calculator
Find polynomial first & second derivatives, evaluate slope f'(x₀), construct tangent line equations, and locate inflection points with full KaTeX steps.
01Set inputsChoose values, units and assumptions.
02Apply the modelf'(x) = d/dx [ax³ + bx² + cx + d] = 3ax² + 2bx + c; Tangent: y - y₀ = f'(x₀)(x - x₀)
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Enter the polynomial coefficients and your evaluation point x₀. The solver differentiates using the power rule, computes instantaneous slope, and builds the tangent equation.
Formula & method
f'(x) = d/dx [ax³ + bx² + cx + d] = 3ax² + 2bx + c; Tangent: y - y₀ = f'(x₀)(x - x₀)
Assumptions & notes
- Applies the power rule d/dx[xⁿ] = n·xⁿ⁻¹ term by term.
- Inflection points occur where the second derivative f''(x) = 0.
- The first derivative represents the instantaneous rate of change.