Accordingly, there are six product rules, two for gradients: (i) V(fg) = fVg+g√ f, . • (ii) V(A B) = Ax (V × B) + B × (V × A) + (A · V)B + (B · V)A, . two for divergences: (iii) ▼ · (ƒA) = ƒ (▼ · A) + A · (V ƒ), (iv) and two for curls: • V. (A × B) = B. (V x A) - A · (V × B), (v) ▼ × (ƒA) = ƒ(V × A) — A × (▼ ƒ), (vi) ▼ × (A × B) = (B. V)A – (A V)B + A(V · B) – B(V · A). - Problem 1.25 (a) Check product rule (iv) (by calculating each term separately) for the functions A = x + 2y ŷ + 3zz; B = 3y ✰ - 2x ŷ. (b) Do the same for product rule (ii). (c) Do the same for rule (vi).
Accordingly, there are six product rules, two for gradients: (i) V(fg) = fVg+g√ f, . • (ii) V(A B) = Ax (V × B) + B × (V × A) + (A · V)B + (B · V)A, . two for divergences: (iii) ▼ · (ƒA) = ƒ (▼ · A) + A · (V ƒ), (iv) and two for curls: • V. (A × B) = B. (V x A) - A · (V × B), (v) ▼ × (ƒA) = ƒ(V × A) — A × (▼ ƒ), (vi) ▼ × (A × B) = (B. V)A – (A V)B + A(V · B) – B(V · A). - Problem 1.25 (a) Check product rule (iv) (by calculating each term separately) for the functions A = x + 2y ŷ + 3zz; B = 3y ✰ - 2x ŷ. (b) Do the same for product rule (ii). (c) Do the same for rule (vi).
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please do parts b and c step by step. I am stuck
Transcribed Image Text:Accordingly, there are six product rules, two for gradients:
(i)
V(fg) = fVg+g√ f,
.
•
(ii) V(A B) = Ax (V × B) + B × (V × A) + (A · V)B + (B · V)A,
.
two for divergences:
(iii)
▼ · (ƒA) = ƒ (▼ · A) + A · (V ƒ),
(iv)
and two for curls:
•
V. (A × B) = B. (V x A) - A · (V × B),
(v)
▼ × (ƒA) = ƒ(V × A) — A × (▼ ƒ),
(vi)
▼ × (A × B) = (B. V)A – (A V)B + A(V · B) – B(V · A).
-
Transcribed Image Text:Problem 1.25
(a) Check product rule (iv) (by calculating each term separately) for the functions
A = x + 2y ŷ + 3zz;
B = 3y ✰ - 2x ŷ.
(b) Do the same for product rule (ii).
(c) Do the same for rule (vi).
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