for `x > 1` if `(2x)^(2y)=4e^(2x-2y)` then `(1+log_e 2x)^2 (dy)/(dx)`

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

If y=e^(x) log (sin 2x), find (dy)/(dx) .

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

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

If y(x) is solution of differential equation satisfying (dy)/(dx)+((2x+1)/x)y=e^(-2x), y(1)=1/2e^(-2) then (A) y(log_e2)=log_e2 (B) y(log_e2)=(log_e2)/4 (C) y(x) is decreasing is (0,1) (D) y(x) is decreasing is (1/2,1)

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

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

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

if x^(y)=e^(x-y) then prove that (dy)/(dx)=(log_(e)x)/((1+log_(e)x)^(2))