Partial Derivative Calculator
Advanced Partial Derivative Calculator for multivariable functions. Compute ∂f/∂x, ∂²f/∂x², and mixed derivatives with step-by-step solutions and visualizations.
What Is It?
A Partial Derivative Calculator computes how multivariable functions change when one variable varies while others remain constant. Essential for:
- Mathematics: Analyzing function behavior
- Physics: Calculating gradients and potentials
- Economics: Modeling marginal changes
- Engineering: Sensitivity analysis
Features symbolic computation, 2D/3D visualizations, and step-by-step solutions.
How to Use
- Enter Function: Use standard notation (e.g.,
x^2*y + sin(y)). - Select Variables: Choose variables for differentiation.
- Set Options:
- Order: First (∂f/∂x), second (∂²f/∂x²), or mixed (∂²f/∂x∂y).
- Evaluation: Optional point values for numerical results.
- Calculate: View symbolic results, steps, and interactive charts.
FAQs
Q: What functions are supported?
A: Polynomials, trigonometric (sin, cos), exponential (exp), logarithmic (log), and more.
Q: Can I evaluate derivatives at specific points?
A: Yes! Enter values for variables to get numerical results.
Q: Why does my 3D plot look flat?
A: For >2 variables, we project to 2D. Use the “Slice” tab to focus on specific variables.
Q: How accurate are the results?
A: Uses symbolic math for exact derivatives (not numerical approximation).
Key Terms Explained
- Partial Derivative (∂f/∂x): Rate of change along one variable axis.
- Gradient (∇f): Vector of all first-order partial derivatives.
- Hessian Matrix: Square matrix of second-order partial derivatives.
- Mixed Derivative (∂²f/∂x∂y): Measures how slope in one direction changes with another variable.
Why Choose This Tool?
- Precision: Symbolic computation avoids rounding errors.
- Clarity: Step-by-step explanations and textbook notation.
- Visual Learning: Charts reveal function behavior intuitively.
- Professional: Trusted by students and researchers worldwide.