The formulas of this problem are useful in thermodynamics. (a) Given f ( x , y , z ) = 0 , find formulas for ∂ y ∂ x z , ∂ x ∂ y z , ∂ y ∂ z x , and ∂ z ∂ x y . (b) Show that ∂ x ∂ y z ∂ y ∂ x z = 1 And ∂ x ∂ y z ∂ y ∂ z x ∂ z ∂ x y = − 1 . (c) If x,y,z are each functions of t , show that ∂ y ∂ z x = ∂ y ∂ t / ∂ z ∂ t x and corresponding formulas for ∂ z ∂ x y and ∂ x ∂ y z .
The formulas of this problem are useful in thermodynamics. (a) Given f ( x , y , z ) = 0 , find formulas for ∂ y ∂ x z , ∂ x ∂ y z , ∂ y ∂ z x , and ∂ z ∂ x y . (b) Show that ∂ x ∂ y z ∂ y ∂ x z = 1 And ∂ x ∂ y z ∂ y ∂ z x ∂ z ∂ x y = − 1 . (c) If x,y,z are each functions of t , show that ∂ y ∂ z x = ∂ y ∂ t / ∂ z ∂ t x and corresponding formulas for ∂ z ∂ x y and ∂ x ∂ y z .
Finite Mathematics & Its Applications (12th Edition)
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