If sin (x + y) = y cos (x + y) then prove that
`dy/dx =-(1 + y^2)/y^2`

If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .

If y=(x)/(x+2) then prove that x(dy)/(dx)=(1-y)y .

If xy log(x + y) = 1 , then prove that (dy)/(dx) = -(y(x^(2)y + x + y))/(x(xy^(2) + x + y)) .

If y = a sinx + b cos x then prove that y^2 + ((dy)/(dx))^2 = a^2 + b^2 .

If x^y = e^(x-y) then prove that (dy)/(dx)=logx/(1+logx)^2 .

If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)