If `f(x)=e^x` , then prove that `f'(x)=e^x`

If f(x)=log_(e)x, then prove that :f(xyz)=f(x)+f(y)+f(z)

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

If g(x)=e^(x) and f(x)=x^(2) then prove that (gof)=e^(x^(2)) and fog=e^(2x)

Let f be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then prove that f(x)=(x^(3))/(3)+x^(2)

If f(x)=|x|e^(x), then at x=0

If f(x)=(e^(x))/(x) , then find f'(x)

If f(x)=e^(x)(x^(2)+1) then find f'(x)

If F(x)= e^sin x then F(0)=

Let f:R to R be defined by f(x) =e^(x)-e^(-x). Prove that f(x) is invertible. Also find the inverse function.

If f(x) = x^(1//x) , " then: f''(e) is