Mathematics · University
Directional derivative along a unit vector · formula reference
Normalize a direction vector before the dot product. Here (3/5,4/5) is already a unit vector.
Formula
Normalize a direction vector before the dot product. Here (3/5,4/5) is already a unit vector.
Dᵤf = ∇f · u
Worked example
For f(x,y) = 7x² + 9y², find the directional derivative at (0,-3) in the unit direction (3/5,4/5). Round the final result to 4 decimal places if needed.
The gradient at the point is (0, -54). Dot this with (3/5,4/5).
-43.2
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
AI-assisted preview; independent educational review required. Level labels describe prerequisites, not accreditation or official curriculum alignment.