Can you derive the exponential property $ [f(x+y) = f(x)\cdot f(y)]$ from $y' = y$?
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
86567
Understanding $\sum_{x = 0}^y x = \frac{y(y + 1)}{2}$ in a step of a proof
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
12092
When can one write $a=v \cdot dv/dx$?
71465
solution of $y' = \exp \left(-\frac yx\right) + \frac yx$
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
62605
How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables?
2315
How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
50451
The linear dependence of exponential functions
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
134880
Is there a difference between $y(x)$ and $f(x)$
16713
Product of an exponential function of IDD variables
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
61144
Derivative of $x^{x^{\cdot^{\cdot}}}$?