Derivative Calculator
Calculate derivatives of common functions step by step.
Enter a function type and coefficients to find the derivative using standard differentiation rules.
Derivative Result
Basic Derivative Rules:
| Function | Derivative |
|---|---|
| x^n | n × x^(n-1) |
| sin(x) | cos(x) |
| cos(x) | -sin(x) |
| tan(x) | sec²(x) |
| e^x | e^x |
| ln(x) | 1/x |
| a × f(x) | a × f’(x) |
Key Rules:
- Power Rule: d/dx [x^n] = n × x^(n-1)
- Constant Multiple: d/dx [c × f(x)] = c × f’(x)
- Sum Rule: d/dx [f(x) + g(x)] = f’(x) + g’(x)
- Product Rule: d/dx [f(x) × g(x)] = f’(x)g(x) + f(x)g’(x)
- Chain Rule: d/dx [f(g(x))] = f’(g(x)) × g’(x)
What is a derivative? The derivative measures the instantaneous rate of change of a function. Geometrically, it gives the slope of the tangent line at any point.