If `xsqrt(1 + y) + ysqrt(1 + x) = 0` show that `(dy)/(dx) = - 1/(1 + x)^2`

If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) , show that (dy)/(dx) - (2x)/(sqrt(1 - x^4)) = 1/(sqrt(1 - x^2))

If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))) , then show that (dy)/(dx) = x/(sqrt(1 - x^4))

If x^y = e^(x + y) , show that (dy)/(dx) = (log x - 2)/((1 - log x)^2)

"If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

If log (sqrt(1 + x^2) - x) = y sqrt(1 + x^2) , show that (1 - x^2) (dy)/(dx) + xy + 1 = 0

If sqrt(1-x^2) + sqrt(1-y^2) = a(x-y), show that dy/dx = sqrt((1-y^2)/(1-x^2))

If x= sqrta^(sin^-1t), y = sqrt(a^(cos^-1t)) , show that dy/dx = -y/x , a > 0

If e^y(x+1)=1 show that (d^2y/dx^2) = (dy/dx)^2 ਹੈ।