Given $f(x+y)=f(x)+f(y)+x^2y+xy^2$ ,find $f'(x)$
71127
How do I find $f(0)$, $f'(0)$, and $f'(x)$ given $f(x+y)=f(x)+f(y)+x^2y+xy^2$ and $\lim_{x\to0}\frac{f(x)}{x}=1$?
148227
Rewriting of functional equation $f(xy)=f(x)+f(y)$
62966
Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
79212
Find the general solution of $y'= a^{x + y}$ where y is the function
10068
$f(x,y)= e^{-\frac{1}{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and $f(0,0)=0$.
31732
If the function $f$ satisfies the equation $f(xf(y)+x)=xy+f(x)$, find $f$
105319
A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$
125788
A function with a property $f(x+y)=f(x)f(y)$
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
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 $f(t)=c\cdot e^t$.
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?
132093
Solve $f(f(x))=f(x)$
53024
$f(x)f(1/x)=f(x)+f(1/x)$
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
23465
When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$