Calculus
Partial Derivatives Calculator
Estimate ∂f/∂x and ∂f/∂y at a specific (x, y) coordinate and inspect the gradient magnitude.
partial derivativegradientmultivariable
Partial Derivatives
Estimate ∂f/∂x and ∂f/∂y for a multivariable function.
∂f/∂x
1
∂f/∂y
1.877583
‖∇f‖
2.127279
Central difference in multiple dimensions
∂f/∂x ≈ [f(x + h, y) − f(x − h, y)] / (2h)
The same stencil applies to ∂f/∂y, giving a quick view of how the surface slopes along each axis.
How to use
- Enter a function f(x, y) using x and y variables.
- Specify the evaluation point (x₀, y₀) and the finite-difference step size.
- Read off partial derivatives and the gradient magnitude.
Example
Input: f(x, y) = x^2 * y + sin(y) at (1, 0.5)
Output: ∂f/∂x ≈ 1.0, ∂f/∂y ≈ 1.5403, ‖∇f‖ ≈ 1.835
FAQ & notes
Can I extend this to more variables?
This panel is tuned for two variables. For higher dimensions, repeat the approach by holding other variables constant.
What step size should I use?
The default (1e-4) balances precision and stability. Reduce it for well-behaved functions or increase it if round-off dominates.