Differentiability of $f(x+y) = f(x)f(y)$
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
6632
Sequence of differentiable functions
16375
Is the function differentiable at $0$?
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
111458
Prove that $f$ is differentiable
71049
Functional equation $f(xy)=f(x)+f(y)$ and continuity
27265
Continuously differentiable map from $\mathbb{R}^{m+n}$ to $\mathbb{R}^n$
26602
Continuity and existence of directional derivatives at all directions of a $f:\mathbb{R}^{2} \to \mathbb{R}$ given by $f(x,y)=\frac{2x^2y}{x^2+y^2}$
18734
Showing that a function is differentiable
121455
$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$
71260
Check differentiability of multivariable functions
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
85623
Proof of continuity implied by differentiability
68409
Consider $f(x,y)=\sup_{θ,φ}\{||e^{i θ }x+ e^{i φ }y||^2: θ,φ∈R\}$ in which $x,y\in\mathbb C^n$
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
3387
Derivative of $f(x)=|x|$
83707
Suppose that $f$ is differentiable on $\mathbb{R}$ and $\lim_{x\to \infty}f'(x)=M$. Show that $\lim_{x\to \infty}f(x+1)-f(x)$ exists and find it.