Showing a functional equation gives rise to exponential function
22303
How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
42745
Validity and Equivalence of two definitions of the real exponential function
71049
Functional equation $f(xy)=f(x)+f(y)$ and continuity
143765
To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$
111556
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?
34888
An MCQ for finding the extremal of the functional $J = \int_{a}^{b} F(x, y, y^{'})$
84318
A problem with the functional $F(\chi) = \int_{\mathbb{R}}(\chi'^2+\chi^2(1-\chi)^2)dx$.
78319
Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0
26677
thoughts about $f(f(x))=e^x$
30533
Showing that this function is infinitely differentiable
104263
How to show that $f'(x)<2f(x)$
95684
Show that $g'(x)+g(x)-2e^x=0$
53998
Solving an exponential inequality problem
99149
Limit of the difference between two exponential functions
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
144090
How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$
139436
Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem