Explanation Given information: The equation is w = f ( r − s s ) Concept and Formula Used: ∂ ∂ x x n = n x n − 1 Partial derivative i.e. keeping one variable constant and differentiate equation with respect to other variable. Calculation: It is given that w = f ( r − s s ) To show r ∂ w ∂ r + s ∂ w ∂ s = 0 start from left hand side and make it equal to right hand side. Differentiate w = f ( r − s s ) first with respect to ‘r’ keeping‘s’ as constant and then with respect to‘s’ keeping ‘r’ as constant. ∂ w ∂ r = ∂ ∂ r ( f ( r − s s ) ) ∂ w ∂ r = f ' ( r − s s ) ∂ ∂ r ( r − s s ) ∂ w ∂ r = f ' ( r − s s ) 1 s ( ∂ r ∂ r − s ∂ ∂ r 1 ) ∂ w ∂ r = f ' ( r − s s ) 1 s ( 1 − 0 ) ∂ w ∂ r = 1 s f ' ( r − s s ) Differentiate w = f ( r − s s ) with respect to ‘s’ keeping ‘r’ as constant. ∂ w ∂ s = ∂ ∂ s ( f ( r − s s ) ) ∂ w ∂ s = f ' ( r − s s ) ∂ ∂ s ( r − s s ) ∂ w ∂ s = f ' ( r − s s ) ( r ∂ ∂ s ( 1 s ) &

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ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 11.5, Problem 47PS

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To Show: r∂w∂r+s∂w∂s=0 for w=f(r−ss)

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Chapter 11.5, Problem 46PS

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r ∂ w ∂ r + s ∂ w ∂ s = 0 for w = f ( r − s s )

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To Show: r∂w∂r+s∂w∂s=0 for w=f(r−ss)

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