If `x=tan(e^(-y))`, then show that `(dy)/(dx)=(-e^y)/(1+x^2)`.

If e^y = e ^(x + y ) , then show that (dy)/(dx) =

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

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

If x ^(y) = e ^(x -y) then (dy)/(dx) =

Find the derivatives of the function If x = log (1 + sin ^(2)y ) show that (dy)/(dx) = (e ^(x))/( sin 2y).

Solve (dy)/(dx)+1=e^(x+y)

The solution of (dy)/(dx)+y=e^(x) is