Derivative Calculator
Differentiate polynomials, trig, and exponential functions symbolically.
3x^3 + 2x^2 - 5x + 7 or sin(x), e^x, ln(x)Derivative Calculator: Mastering the Rate of Change
Our Derivative Calculator makes calculus differentiation fast and accurate. Enter any polynomial like 3x2 + 5x − 7 or a transcendental function like sin(x) or ex and get the symbolic derivative instantly. Optionally supply a numeric x value to evaluate f′(x) at any point.
Differentiation Rules
- Power Rule: d/dx [xn] = n·xn−1
- Constant Rule: d/dx [c] = 0
- Trigonometric: d/dx[sin x] = cos x, d/dx[cos x] = −sin x
- Exponential & Log: d/dx[ex] = ex, d/dx[ln x] = 1/x
Why Derivatives Matter
In physics, the derivative of position gives velocity; in economics it gives marginal revenue. Machine learning gradient descent relies entirely on derivatives to train neural networks. The derivative is the universal language of change across every STEM discipline.
How to Use This Tool
Write polynomials as ax^n terms separated by + or −. For transcendentals use sin(x), cos(x), e^x, ln(x), or sqrt(x). Multi-term polynomials are automatically parsed term by term using the Power Rule.