Question

Find dy/dx if x^2+2xy+xy^2=5

Answer 1

Answer:

dy / dx = - ( 2x + 2y + y² ) / ( 2x(1+y) )

Step-by-step explanation:

x² + 2xy + xy² = 5

⇒ d( x² + 2xy + xy²) = d(5)

⇒ d(x²) + d(2xy) + d(xy²) = 0

⇒ 2x dx + ( 2y dx + 2x dy ) + ( y² dx + x d(y²) ) = 0

⇒ 2x dx + 2y dx + 2x dy + y² dx + 2xy dy = 0

⇒ ( 2x + 2y + y² ) dx + 2x ( 1 + y ) dy = 0

⇒ 2x ( 1 + y ) dy = -( 2x + 2y + y² ) dx

⇒ dy / dx = - ( 2x + 2y + y² ) / ( 2x(1+y) )

Hope that helps