Answer:
The gradient of vector
∇g = i⁻(2 x -6 ) + j⁻ (2y)
The gradient of vector at the point (2 ,6) is
( ∇g)₍₂,₆) = (-2) i⁻ + (12) j⁻
Step-by-step explanation:
<u><em>Explanation</em></u>:-
Given g (x, y) = x² +y² -6x ...(i)
The gradient of vector
∇g =( i⁻ δ/δx + j⁻ δ/δy+ k⁻δ/δZ)g
= ( i⁻ δg/δx + j⁻ δg/δy+ k⁻δg/δZ) .....(ii)
Differentiating equation (i) partially with respective to 'x' , treated 'y' as constant.
δg/δx = 2x - 6
Differentiating equation (i) partially with respective to 'x' , treated 'y' as constant.
δg/δy = 2y
<u><em>Step(ii)</em></u>:-
The gradient of vector
∇g = i⁻(2 x -6 ) + j⁻ (2y)
At the point ( 2,6)
( ∇g)₍₂,₆) = i⁻(2 (2) -6 ) + j⁻ (2(6))
( ∇g)₍₂,₆) = i⁻(-2) + j⁻ (12)
