Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Find dy/dx by implicit differentiation. 7x2 + 5xy − y2 = 8?

9 Answers

Relevance
  • 4 weeks ago
    Favourite answer

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

    =>

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

    =>

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

    =>

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

    • Commenter avatarLog in to reply to the answers
  • Como
    Lv 7
    4 weeks ago

    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)

    • Commenter avatarLog in to reply to the answers
  • Philip
    Lv 6
    4 weeks ago

    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).

    • Commenter avatarLog in to reply to the answers
  • 4 weeks ago

    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 )

    —————————————

    • Commenter avatarLog in to reply to the answers
  • What do you think of the answers? You can sign in to give your opinion on the answer.
  • 4 weeks ago

    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)

    • Commenter avatarLog in to reply to the answers
  • 4 weeks ago

    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)

    • Commenter avatarLog in to reply to the answers
  • 4 weeks ago

    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

    • Commenter avatarLog in to reply to the answers
  • Bryce
    Lv 7
    1 month ago

    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)

    • Commenter avatarLog in to reply to the answers
  • 1 month ago

    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)

    • Vaman
      Lv 7
      4 weeks agoReport

      Good answer.

    • Commenter avatarLog in to reply to the answers
Still have questions? Get answers by asking now.