Question

If x²+6xy+y²=10 then show that d²y/dx²= 80/(3x+y)³

Answer 1

Answer:

Given,

x^2 + 6xy + y^2 = 10

=> 2x + 6y + 6x(dy/dx) + 2y(dy/dx) = 0

=> (dy/dx) = -(x+3y)/(3x+y)

=> d2y/dx2 = -[(3x+y)(1+3dy/dx) – (x+3y)(3+dy/dx)]/(3x+y)2

Now put,

=> dy/dx = -(x+3y)/(3x+y)

=> dy^2/dx^2 = 80/ (3x+y)^3

LHS = RHS

Hence, verified and proved.

Answer 2

Answer:

Step-by-step explanation:

plz mark me  as the brainliest

=x² +6xy+y²

dy/dx=2x+6+6×dy/dx+2y×dy/dx

=dy/dx(2y+6)+2x+6

-6-2x=dy/dx(2y+6)

dy/dx=(-6-2x)/(2y+6)

=2(-3-x)/2(y+3)

=-3-x/y+3

d²y/dx²=[(y+3)(-1)+(3-x)(1)]/[y²+6x+9]

        =  -y-3+3-x/y+3

         =-y-x/y+3