Derivative Calculator
Calculate derivatives with step-by-step solutions
Function Input
Input Format:
- • Use ^ for exponents (e.g., x^2)
- • Include all terms (e.g., 2x + 1)
- • Spaces are optional
- • Constants can be written as numbers
Understanding Derivatives
Basic Rules
- • Power Rule: d/dx(x^n) = nx^(n-1)
- • Constant Rule: d/dx(c) = 0
- • Sum Rule: d/dx(f + g) = f' + g'
- • Constant Multiple: d/dx(cf) = c·f'
Applications
- • Rate of change
- • Slope of tangent lines
- • Optimization problems
- • Motion analysis
Common Derivatives
Basic Functions
- • d/dx(x) = 1
- • d/dx(x²) = 2x
- • d/dx(x³) = 3x²
- • d/dx(1) = 0
Examples
- • d/dx(2x² + 3x) = 4x + 3
- • d/dx(x³ - 2x + 1) = 3x² - 2
- • d/dx(5x⁴) = 20x³
- • d/dx(-x² + 4) = -2x
Tips
- • Break down complex terms
- • Apply rules one at a time
- • Check your work
- • Simplify final answer