Find all differentiable functions $f$ such that $f(f(x))=f'(x)$
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
139019
Polynomial satisfying $f(x) = f'(x) \cdot f''(x)$
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
104278
Finding function $f(x)$ which satisfy given functional equation
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
106748
Number of functions $f : A \to A$ such that $f(f(x))=f(x)$
130748
Infinitely differentiable function with given zero set?
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
23485
Solving $\forall x \in \mathbb{R}_+^*, f'(x) = f\left(\frac1{x}\right)$
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
156536
Defining functions as derivatives
139216
Use the definition of derivative to find $f'(x)$ for $f(x) = x^{1/2}$.