What is the 𝑑𝑦/𝑑x for the following implicit functions

Question

a. 𝑥² + 𝑦² = (𝑥 + 𝑦)²

b. 𝑦 cos 𝑥 = (𝑥 − 𝑦)²

c. 𝑦𝑒^𝑥 − 𝑒^𝑦 cos 𝑦 = 5

d. (𝑥² + 𝑦² )³ = 𝑥 + y

Answer 1

desmos.com/calculator/drbbiblmwl

Answer 2

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

2x + 2yy' = 2(x+y)(1 + y')

x + yy' = x +y +xy' + yy'

xy' = -y

y' = -y/x

or

expand the original equation, cancel terms to get

0 = 2xy then take the derivative

0 = 2xy' + 2y

xy' = -y

y' = -y/x

dy/dx = -y/x