Compute partial derivatives of multivariable functions with respect to x, y, or z. Get step-by-step rule applications, gradient vectors, numerical evaluations, and a gradient magnitude heatmap.
Enter f(x,y) or f(x,y,z) and choose differentiation variable
Use: x y z + - * / ^ sin cos tan exp sqrt log abs · Constants: PI E
∂f/∂x =
Gradient Vector ∇f
Numerical approximations using central difference method
Gradient Magnitude |∇f|
x → right, y → up
Power Rule
∂/∂x [xⁿ] = n·xⁿ⁻¹
Chain Rule
∂/∂x [f(g)] = f'(g)·∂g/∂x
Product Rule
∂/∂x [fg] = f·∂g/∂x + g·∂f/∂x
Gradient
∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)