Find if $|x|^\alpha \sin(\frac{1}{x})$ is continuous and differentiable.
121848
If $f(x)=\begin {cases} x^a\sin (1/x) & x\not =0 \\ 0 & x =0 \end {cases}$ is continuous but not differentiable at $x=0$ find $a$
103757
how can I prove that $\frac{\arctan x}{x }< 1$?
88259
prove that $\frac{1}{x}$ is not uniformly continuous on $(0,1)$
18734
Showing that a function is differentiable
96112
Differentiating $ \left( 1 - \frac {1}{x} \right)^x $
87131
Discontinuous at rationals and differentiable at irrationals?
149827
show that $x\sin\left(\frac{1}{x}\right)$ is uniformly continuous on $(0,1)$
111470
Proof of differentiability of $f(x)$
155170
Proving $\sin(x^2)$ Continuous but Not Uniformly Continuous with non-standard Definition
96450
If $f(x)$ is continuous and differentiable function , prove that $f(x) \geq e^{3x}, \forall x \geq 0$
17310
Can $f(x)=|x|^3$ be differentiated
158681
How to show that $e^x$ is differentiable?
152105
When is $x^{\alpha}\sin(x^{\beta})$ uniformly continuous for $\alpha, \beta > 0$?
105084
Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
43874
Differentiability implies continuity - A question about the proof
137527
if $f(x)$ is differentiable at a x, prove that: $\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$
4636
How to show that $f$ is differentiable at $x=0.$