Work out directional derivative instantly with clear inputs, formula shown and shareable results.
The directional derivative is the gradient dotted with a unit direction vector: D_u f = ∇f · û. It reaches its maximum |∇f| when the direction aligns with the gradient and is zero along a level curve.
Directional derivative
D_u f = ∇f · û = |∇f|·cos θ
The unit direction is (0.7071068, 0.7071068), so the derivative is 7/√2 ≈ 4.9497475 — about 99% of the maximum 5.
Yes, otherwise the answer scales with the arbitrary length of the vector rather than measuring a rate per unit distance.