Derivative Calculator
Calculate the numerical derivative of a function at a specific point.
f'(x) at this point
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Enter function and point
f(x)
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Derivative Formula
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Derivative Rules
The derivative measures the rate of change of a function. It represents the slope of the tangent line at any point.
Basic Differentiation Rules
Power Rule: d/dx(x^n) = nx^(n-1)
Constant: d/dx(c) = 0
Sum: d/dx(f+g) = f' + g'
Constant: d/dx(c) = 0
Sum: d/dx(f+g) = f' + g'
Derivatives of Common Functions
| Function | Derivative |
|---|---|
| sin(x) | cos(x) |
| cos(x) | -sin(x) |
| tan(x) | sec²(x) |
| e^x | e^x |
| ln(x) | 1/x |
| a^x | a^x · ln(a) |
Advanced Rules
- Product Rule: (fg)' = f'g + fg'
- Quotient Rule: (f/g)' = (f'g - fg')/g²
- Chain Rule: d/dx[f(g(x))] = f'(g(x))·g'(x)
Frequently Asked Questions
What is a derivative?
A derivative measures the instantaneous rate of change of a function. It tells you how fast the output changes when the input changes slightly.
How do I find the derivative of a polynomial?
Use the power rule: multiply each term by its exponent, then reduce the exponent by 1. For 3x² + 2x + 1, the derivative is 6x + 2.