Understand and calculate partial derivatives of multivariable functions.
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Derivatives (Example)
For simple power rule functions like xⁿyᵐ:
∂f/∂xnxⁿ⁻¹yᵐDerivative w.r.t x
∂f/∂ymxⁿyᵐ⁻¹Derivative w.r.t y
Example Calculation:
f(x, y) = x² + 3xy + y²
∂f/∂x = 2x + 3y (Treat y as constant)
∂f/∂y = 3x + 2y (Treat x as constant)
About this calculator
What is a Partial Derivative?
A partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant. It represents how the function changes as that specific variable changes.
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Pro Tips
Treat all other variables as constants when differentiating with respect to one variable.
The notation ∂ is called 'del' or 'partial'.
Gradient vectors are composed of partial derivatives.
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Fun Facts
"Partial derivatives are fundamental in physics, especially in fields like thermodynamics and fluid dynamics."
"The concept was developed in the 18th century as calculus expanded to higher dimensions."
