If `y=f(x)` then `dy/dx = f'(x)`, therefore, let `y=f{g(x)}`, then `f'{g(x)}` will be denoted by

If y = f(x) (dy)/dx=f'(x) therfore y=f{g(x)} then f'{g(x)} will be denoted by

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])

Let y=f(x) satisfies (dy)/(dx)=(x+y)/(x) and f(e)=e then the value of f(1) is

Let y=f(x) satisfies (dy)/(dx)=(x+y)/(x) and f(e)=e then the value of f(1) is

If y=f(x) and x=g(y) are inverse of each other. Then g'(y) and g"(y) in terms of derivative of f(y) is A. -(f"(x))/([f'(x)]^(3)) B. (f"(x))/([f'(x)]^(2)) C. -(f"(x))/([f'(x)]^(2)) D. None of these

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

Let f(x+y)=f(x)f(y) and f(x)=1+(sin2x)g(x) , where g(x) is continuous. Then f'(x) is equal to :