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

If e^(g(y)) - e^(-g(y)) = 2 f(x) then (dy)/(dx) =

If e^(g(y))-e^(-g(y))=2f(x) then (dy)/(dx)=

A: If y = x ^(y) then (dy)/(dx) = (y ^(2))/(x(1- log y )) If y = f (x) ^(y), then (dy)/(dx) = (y ^(2) f '(x))/(f (x) [1- ylog f (x)])= (y ^(2) f'(x))/(f (x) [1- log y])

If y = (f(x))/(g(x)) , where f (x) and g (x) are two differentiable functions, write the formula for determining (dy)/(dx) . Applying the foumula, find (dy)/(dx) for the function y = (x-2)/(x +2) , mention the value of x for which it is not possible to find (dy)/(dx) .

Let the function f(x) and g(x) be inverse of each other then f(g(x)=g(f(x))=xf'(g(x))g'(x)=g'(f(x))f'(x)=1 If (dy)/(dx) exist and (dy)/(dx)!=0, then (dx)/(dy)=(1)/(dy) or (dy)/(dx)*(dx)/(dy)=1 or (dy)/(dx)=(1)/(dx)[(dx)/(dy)!=0]

If y=e^(x) + x f i n d dy/dx.

If f(x) and g(x) are two solutions of the differential equation (a(d^(2)y)/(dx^(2))+x^(2)(dy)/(dx)+y=e^(x),thenf(x)-g(x)^(@) is the solution of