How to solve
The gradient packages all first partial derivatives into a vector ∇f = ⟨f_x, f_y⟩. It points in the direction of steepest increase and its components are exactly those partial slopes.
Steps
- Compute f_x by treating y as constant.
- Compute f_y by treating x as constant.
- Write ∇f = ⟨f_x, f_y⟩.
Example
If f(x, y) = x² + 2y², find ∇f.
- f_x = 2x, f_y = 4y.
- ∇f = ⟨2x, 4y⟩.
Answer: <2x, 4y>
How to type answers
- Enter <2x, 4y> with angle brackets
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