Let f(x) be a function satisfying `f(x+y)=f(x)f(y)` for all `x,y in R` and f(x)=1+xg(x) where `lim_(x to 0) g(x)=1`. Then f'(x) is equal to

Let f(x) be a function satisfying f(x+y)=f(x)f(y) for all x,y in R and f(x)=1+xg(x) where underset(x to 0)lim g(x)=1 . Then f'(x) 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)=

Let f be a function satisfying f(x+y)=f(x)+f(y) for all x,y in R. If f(1)=k then f(n),n in N 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