Partial Derivative Calculator

Calculate partial derivatives of f(x,y) = axy + bx² + cy² + d. Find df/dx, df/dy, and the gradient magnitude.

Coefficient of xy (a)

Coefficient of x² (b)

Coefficient of y² (c)

Constant (d)

x Value

y Value

Tab to move between fields

∂f/∂x

∂f/∂y

f(x,y)6

|∇f|8.6023

How to Use This Calculator

Select the function type (e.g., f(x,y) = axⁿyᵐ or a product/composition of x and y terms).
Enter the function parameters and the point (x₀, y₀) at which to evaluate the partial derivatives.
∂f/∂x is computed by treating y as a constant and differentiating with respect to x only.
∂f/∂y is computed by treating x as a constant and differentiating with respect to y only.
Together, (∂f/∂x, ∂f/∂y) form the gradient vector ∇f, which the Gradient Calculator can use directly.
Mixed partial ∂²f/∂x∂y is shown where applicable; by Clairaut's theorem it equals ∂²f/∂y∂x for smooth functions.

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