Derivative Calculator
Solve derivative problems step-by-step with our free calculator. See formulas, worked examples, and clear explanations.
Reviewed by Manoj Kumar, Mathematics Educator
Reviewed by Manoj Kumar, Mathematics Educator
Formula
f'(x) ≈ [f(x+h) - f(x-h)] / (2h) | f''(x) ≈ [f(x+h) - 2f(x) + f(x-h)] / h²
Central difference formula for numerical differentiation. The first derivative uses the symmetric difference quotient (error O(h²)). The second derivative uses the second-order central difference.
Worked Examples
Example 1: d/dx(x³) at x=2
Problem:f(x) = x³, find derivative at x = 2
Solution:f'(x) = 3x² → f'(2) = 12
Result:f'(2) ≈ 12.00000000
Example 2: Derivative of sin(x) at x=0
Problem:f(x) = sin(x), find derivative at x = 0
Solution:f'(x) = cos(x) → f'(0) = cos(0) = 1
Result:f'(0) ≈ 1.00000000
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy