Explanation Formula used: Product Rule and Chain Rule: Let u and v be two differentiable functions then, d d x ( u v ) = u d v d x + v d u d x and d d x [ u ( v ( x ) ) ] = d d x [ u ( v ( x ) ) ] ⋅ d d x [ v ( x ) ] Calculation: It is given that the law of cosines equation is c 2 = a 2 + b 2 − 2 a b cos C where a, b, c are magnitudes and C is the angle. Write c as a 2 + b 2 − 2 a b cos C . Differentiate c = a 2 + b 2 − 2 a b cos C partially with respect to a as follows. ∂ c ∂ a = ∂ ∂ a ( a 2 + b 2 − 2 a b cos C ) = 1 2 a 2 + b 2 − 2 a b cos C ∂ ∂ a ( a 2 + b 2 − 2 a b cos C ) = 1 2 a 2 + b 2 − 2 a b cos C ( 2 a − 2 b cos C ∂ ∂ a a ) = 2 a − 2 b cos C 2 a 2 + b 2 − 2 a b cos C That is, ∂ c ∂ a = a − b cos C a 2 + b 2 − 2 a b cos C . At C = 60 ° , the value of ∂ c ∂ a becomes, ∂ c ∂ a | C = 60 ° = a − b cos 60 ° a 2 + b 2 − 2 a b cos 60 ° = a − b ( 1 2 ) a 2 + b 2 − 2 a b ( 1 2 ) = 2 a − b 2 a 2 + b 2 − a b Differentiate c = a 2 + b 2 − 2 a b cos C partially with respect to b as follows

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 29.3, Problem 36E

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The values of the partial derivatives ∂c∂a and ∂c∂b at C=60°.

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Chapter 29.3, Problem 35E

Chapter 29.3, Problem 37E

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Chapter 29 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

Ch. 29.1 - Practice Exercise If f(x, y) = 4xy2 – 3x2y, find...Ch. 29.1 - Prob. 1E Ch. 29.1 - Prob. 2E Ch. 29.1 - Prob. 3E Ch. 29.1 - Prob. 4E Ch. 29.1 - Prob. 5E Ch. 29.1 - Prob. 6E Ch. 29.1 - Prob. 7E Ch. 29.1 - Prob. 8E Ch. 29.1 - Prob. 9E

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The values of the partial derivatives ∂ c ∂ a and ∂ c ∂ b at C = 60 ° .

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The values of the partial derivatives ∂c∂a and ∂c∂b at C=60°.

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Chapter 29 Solutions