For the function h(x, y) = (7x + 5y)/(6xy -1), find partial differential h/parti

Question

For the function h(x, y) = (7x + 5y)/(6xy -1), find partial differential h/partial differential x and partial differential h/partial differential y Choose the correct answer for partial differential h/partial differential x A. 7x + 5y/(6xy -1)^2 B. - 7 -730y^2/(6xy - 1)^2 C. 7x + 30y/(6xy - 1)^2 D. - 7 - 30y/(6xy -1)^2 Choose the correct expression for partial differential h/partial differential y A. 5 - 7x^2/(6xy -1)^2 B. -5 + 42x^2/(6xy - 1)^2 C. 5x - 42y^2/(6xy - 1)^2 D. -5 - 42x^2/(6xy - 1)^2

Explanation / Answer

We have given h(x,y)=(7x+5y)/(6xy-1)

partial derivating with respect to x and treating y as constant

apply the quotient rule d(u/v)/dx =[v(du/dx)-u(dv/dx)]/v^2

h/x =[(6xy-1)(7)-(7x+5y)(6y)]/(6xy-1)2

=[42xy-7-42xy-30y2]/(6xy-1)2

h/x =(-7-30y2)/(6xy-1)2

answer is B

partial derivating with respect to y and treating x as constant

apply the quotient rule d(u/v)/dy =[v(du/dy)-u(dv/dy)]/v^2

h/y =[(6xy-1)(5)-(7x+5y)(6x)]/(6xy-1)2

=[30xy-5-42x^2-30xy]/(6xy-1)2

=[-5-42x^2]/(6xy-1)2

h/y =(-5-42x^2)/(6xy-1)2

answer is D

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