What is derivative a of a continuous function such that $f(x+y) = f(x) +f(y)$?
75266
$f(a+b)=f(a)+f(b)$ but $f$ is not linear
26602
Continuity and existence of directional derivatives at all directions of a $f:\mathbb{R}^{2} \to \mathbb{R}$ given by $f(x,y)=\frac{2x^2y}{x^2+y^2}$
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
78834
if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $
154881
Question on differentiability of a continuous function
124444
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
43667
Is $f(x,y(x))$ a function of two variables? If so, how is that possible?
125788
A function with a property $f(x+y)=f(x)f(y)$
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
145368
How to show $f:Y\to X^{+}$ is continuous?
49705
Is $f(x,y)=(x+2y+y^2+|xy|, 2x+y+x^2+|xy|)$ differentiable?
79212
Find the general solution of $y'= a^{x + y}$ where y is the function
105084
Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
32856
Functional equations $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
71049
Functional equation $f(xy)=f(x)+f(y)$ and continuity