Prove that $f(x)=x^2 \sin\left ( \frac{1}{x} \right )$ for $x \neq 0$, $f(0)=0$ is differentiable on $\mathbb{R}$.
59956
Show that the function $g(x) = x^2 \sin(\frac{1}{x}) ,(g(0) = 0)$ is everywhere differentiable and that $g′(0) = 0$
149827
show that $x\sin\left(\frac{1}{x}\right)$ is uniformly continuous on $(0,1)$
145173
$f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
49705
Is $f(x,y)=(x+2y+y^2+|xy|, 2x+y+x^2+|xy|)$ differentiable?
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
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 $a$
68854
Proving $\mathcal{F}\left(\frac{d^n}{dx^n} f(x)\right)=(ik)^n\mathcal{F}(f(x))$.
105068
Proving that the function is differentiable and $f'(0)=0$
86860
Continuity of differentiable function $x^2\sin(1/x)$
137527
if $f(x)$ is differentiable at a x, prove that: $\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
143491
Show that $f$ is differentiable on $(−1, 1)$.
26373
Uniform continuity of $f(x) = x \sin{\frac{1}{x}}$ for $x \neq 0$ and $f(0) = 0.$
52858
Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $