Question

Please answer it correctly. Don't give irrevelant answer. Please show it in process.
Thank you​

Answer 1

Answer:

Step-by-step explanation:

x (1+y)^(1/2) = -y (1+x)^(1/2) ------ (a)

SQUARING

(x^2)(1+y) = (y^2)(1+x)

x^2 + y(x^2) - y^2 - x(y^2) = 0

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(x-y)(x+y) + xy(x-y) = 0

(x-y)(x+y+xy) = 0

x=y doesn't satisfy (a)

So

x+y+xy = 0

y = -x / (1+x)

Differentiating w.r.t x

(dy/dx) = -1 / [ (1+x)^2 ]

____________ii method_________

dydx=−1(x+1)2

Explanation:

x√1+y+y√1+x=0

x√1+y=−y√1+x

x2⋅(1+y)=(−y)2⋅(1+x)

x2⋅(1+y)=y2⋅(1+x)

x2+x2⋅y=y2+y2⋅x

x2−y2=y2⋅x−x2⋅y

(x+y)⋅(x−y)=−xy⋅(x−y)

x+y=−xy

x=−xy−y

x=−y⋅(x+1)

y=−xx+1

dydx=−1⋅(x+1)−(−x)⋅1(x+1)2

dydx=−1(x+1)2

1) I solved this equation for y.

2) I differentiated both sides.

_________iii method __________

x√ (1+y) = -y √(1+x)

Sqare both sides

x^2(1+y) = (y^2)(1+x)

x^2 + y(x^2) = y^2 + x(y^2)

(x-y)(x+y) + xy(x-y) = 0

(x-y)(x+y+xy) = 0

x can't be equal to y , therefore

x+y+xy = 0

y = -x / (1+x)

Differentiate eqn w.r.t x

dy/dx = -1/(1+x)^2

____________________________

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Answer 2

Answer:

stop thanking my answers and setting Sherlock as your display picture. It's annoying.