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

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

If f^(1)(x)=(1)/(1+(ln x)^(2)) and y=f(e^(tan x)) then (dy)/(dx) is equal to

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 x+y=tan^(-1)y" and "(d^(2)y)/(dx^(2))=f(y)(dy)/(dx) , then f(y)=

If y = f(x^2) and f'(x) = e^(sqrtx) , then find (dy)/(dx)

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

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

If f(x) and g(x) are functions such that f(x + y) = f(x) g(y) + g(x) f(x), then in |(f(alpha),g(alpha),f(alpha+theta)),(f(beta),g(beta),f(beta+theta)), (f(lambda),g(lambda),f(lambda+theta))| is independent of