Prove that a function is differentiable at $x=0$
4636
How to show that $f$ is differentiable at $x=0.$
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
94193
determine whether $f(x, y) = \frac{xy^3}{x^2 + y^4}$ is differentiable at $(0, 0)$.
85623
Proof of continuity implied by differentiability
44880
Prove that the derivative of an even differentiable function is odd, and the derivative of an odd is even.
148737
Is $|xy|$ differentiable in $(0,0)$?
26388
proof that function is constant
112898
Derivative of sin(x)/x at $0$ by definition of derivative
96973
If $F(0,0)=0$ and $F(x,y)= \frac{xy}{x^2+y^2}$ for $(x,y)\neq (0,0)$ then $F$ is differentiable at $(0,0)$?
117770
Let $\displaystyle f$ be differentiable, $\displaystyle f(x)=0$ for $|x| \geq 10 $ and $g(x)=\sum_{k \in \mathbb Z}f(x+k).$
30860
Prove that $f(x)=0$ in $[-1,1]$.
60321
Use the definition of derivative to prove $\lim_{x\to 0}\ln(x+1)/x =1$
31051
Is $f(x,y)=(xy)^{2/3}$ differentiable at $(0,0)$?
115635
Differentiability of antiderivative and continuity of derivative
6417
Can a function be differentiable at the end points of its (closed interval) domain?
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$