Verified answer

7x^2+5xy-y^2=8

=>

14x+5y+5xy'-2yy'=0

=>

(5x-2y)y'=-(14x+5y)

=>

y'=-(14x+5y)/(5x-2y)

7x²  +  (5x) y - y² = 8

14x  + 5y + dy/dx (5x)  - 2y dy/dx   =  0

( 5x  - 2y ) dy/dx   = - (5y  + 14x)

dy/dx   =  - (5y  + 14x) / (5x  - 2y)

7x^2 +5xy -y^2 = 8. Implicit differentiation gives 14x +5(xy'+y) = 2yy', ie., 14x+5y =

(2y-5x)y'. Then y' = (14x+5y)/(2y-5x) = -(14x+5y)/(5x-2y).

7x² + 5xy - y² = 8

14x + 5xy’ + 5y - 2yy’ = 0

( 2y - 5x )y' = ( 5y + 14x )

y' = ( 5y + 14x )/( 2y - 5x )

dy/dx = ( 5y + 14x )/( 2y - 5x )

—————————————

14x + 5y + 5xdy/dx - 2ydy/dx = 0

14x + 5y + dy/dx (5x - 2y) = 0

dy/dx((5x - 2y) = -14x - 5y

dy/dx = (-14x - 5y) / ((5x - 2y)

d(7x²)/dx = 14x

d(5xy)/dx = 5y + 5x(dy/dx)

d(y²)/dx = 2y(dy/dx)

d(8)/dx = 0

7x² + 5xy - y²= 8, so

14x + 5y + 5x(dy/dx) - 2y(dy/dx) = 0

(5x - 2y)(dy/dx) = -14x - 5y

dy/dx = (-14x - 5y)/(5x - 2y)

7x^2 + 5xy − y^2 = 8

14x + 5(y * 1 + xdy/dx) - 2ydy/dx = 0

14x + 5y + 5xdy/dx - 2ydy/dx = 0

 5xdy/dx - 2ydy/dx = - 14x - 5y

dy/dx(5x - 2y) = - 14x - 5y

............... - 14x - 5y...............14x + 5y

dy/dx =  ------------------- or - ---------------- answer//

................... 5x - 2y.................5x - 2y

7x² + 5xy - y²= 8

14x + 5x*dy/dx + 5y - 2y*dy/dx= 0

dy/dx(5x - 2y)= -(14x + 5y)

dy/dx= -(14x + 5y)/(5x - 2y)

7x² + 5xy - y² = 8

7x² + 5xy - y² - 8 = 0

7x² + 5xy - y² - 8 = 0 → when x is constant: → (5x - 2y).dy = 0

7x² + 5xy - y² - 8 = 0 → when y is constant: → (14x + 5y).dx = 0

(5x - 2y).dy + (14x + 5y).dx = 0

(5x - 2y).dy = - (14x + 5y).dx

dy/dx = - (14x + 5y)/(5x - 2y)