Partial Derivative Calculator
Calculate partial derivatives of multivariable functions with detailed step-by-step solutions supporting polynomial, trigonometric, exponential, and logarithmic functions
Function and Variable
Supported: +, -, *, ^, sin(), cos(), tan(), ln(), e^x, variables x, y, z
Partial Derivative Rules
Basic Rules
- • Constant Rule: ∂/∂x[c] = 0
- • Power Rule: ∂/∂x[x^n] = nx^(n-1)
- • Sum Rule: ∂/∂x[f + g] = ∂f/∂x + ∂g/∂x
- • Product Rule: ∂/∂x[fg] = f·∂g/∂x + g·∂f/∂x
Common Functions
- • ∂/∂x[sin(x)] = cos(x)
- • ∂/∂x[cos(x)] = -sin(x)
- • ∂/∂x[e^x] = e^x
- • ∂/∂x[ln(x)] = 1/x
Usage Tips
•
Use ^ for exponents: x^2, y^3
•
Use * for multiplication: 2*x*y
•
Treat other variables as constants
•
Use parentheses for complex expressions
•
Supports basic trigonometric and exponential functions
Examples
Basic Examples
∂/∂x[x²] = 2x
∂/∂x[xy] = y
∂/∂y[x²y³] = 3x²y²
∂/∂x[sin(x)] = cos(x)
Advanced Examples
∂/∂x[x²+y²] = 2x
∂/∂y[x²+y²] = 2y
∂/∂x[e^x·y] = e^x·y
∂/∂x[ln(x)+y²] = 1/x