Let `f(xy)=f(xy) f(y)"for all"x gt 0, y gt 0 and f(1+x)=1+x[1+g(x)],"where "lim_(x to 0) , where g(x),"then " int(f(x))/(f'(x)) dx is`

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to

If f(x+y)=f(x)f(y) for all x, y and f(x)=1+xg(x) , where lim_(xto0)g(x)=1 . Show that f'(x)=f(x) .

Let f:R to R be a function given by f(x+y)=f(x) f(y)"for all "x,y in R "If "f(x)=1+xg(x),log_(e)2, "where "lim_(x to 0) g(x)=1. "Then, f'(x)=

Let f:R to R be a function given by f(x+y)=f(x) f(y)"for all "x,y in R "If "f(x)=1+xg(x),log_(e)2, "where "lim_(x to 0) g(x)=1. "Then, f'(x)=

If f(x + y) = f(x)f(y) for all x, y and and f(x) = 1 + x g(x), where lim_(xrarr0)g(x)=1 ) , show that f'(x) = f(x).

Calculate lim_(x to 0) f(x) , where f(x) = (1)/(x^(2)) for x gt 0