Derivative Calculator
A derivative measures the instantaneous rate of change of a function — the slope of the tangent line at any point. Derivatives are the foundation of differential calculus and are used in physics (velocity, acceleration), economics (marginal cost), and optimisation.
- 1Power rule: d/dx[xⁿ] = n·xⁿ⁻¹
- 2Chain rule: d/dx[f(g(x))] = f'(g(x)) · g'(x)
- 3Product rule: d/dx[f·g] = f'g + fg'
- 4Common derivatives: d/dx[sin x] = cos x, d/dx[eˣ] = eˣ, d/dx[ln x] = 1/x
f(x) = x³=f'(x) = 3x²Power rule: bring down exponent, reduce by 1
f(x) = sin(x)=f'(x) = cos(x)Standard trigonometric derivative
f(x) = x² + 3x + 5=f'(x) = 2x + 3Derivative of constant = 0
| Function f(x) | Derivative f'(x) |
|---|---|
| xⁿ | nxⁿ⁻¹ |
| eˣ | eˣ |
| ln(x) | 1/x |
| sin(x) | cos(x) |
| cos(x) | −sin(x) |
| tan(x) | sec²(x) |
🔒
100% 무료
가입 불필요
✓
정확
검증된 공식
⚡
즉시
즉각적인 결과
📱
모바일 지원
모든 기기