Derivative Calculator
Calculate the derivative (dy/dx) of common mathematical functions symbolically.
Enter values and click Calculate.
Formulas Used
Power Rule: d/dx [axn] = an·xn−1
Sine: d/dx [a·sin(bx)] = ab·cos(bx)
Cosine: d/dx [a·cos(bx)] = −ab·sin(bx)
Tangent: d/dx [a·tan(bx)] = ab·sec²(bx)
Exponential: d/dx [a·ebx] = ab·ebx
Natural Log: d/dx [a·ln(bx)] = a/x
Assumptions & References
- All derivatives are with respect to x using standard calculus differentiation rules.
- Trigonometric inputs for numerical evaluation are in radians.
- For ln(bx), the domain requires x > 0 and b ≠ 0.
- For tan(bx), the derivative is undefined where cos(bx) = 0 (i.e., bx = π/2 + nπ).
- The chain rule is applied for composite functions (e.g., sin(bx), e^(bx), ln(bx)).
- Reference: Stewart, J. Calculus: Early Transcendentals, 8th ed. Cengage Learning.
- Reference: Wikipedia – Differentiation Rules