Show that $x^2\sin(\tfrac{1}{x})$ is classically differentiable.
59956
Show that the function $g(x) = x^2 \sin(\frac{1}{x}) ,(g(0) = 0)$ is everywhere differentiable and that $g′(0) = 0$
119209
Differentiation wrt parameter $\int_0^\infty \sin^2(x)\cdot(x^2(x^2+1))^{-1}dx$
145173
$f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
69803
An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$
149827
show that $x\sin\left(\frac{1}{x}\right)$ is uniformly continuous on $(0,1)$
99795
Derivative of piece-wise function given by $x\sin\frac1x$ at $x=0$
59911
Looking for help with a proof that n-th derivative of $e^\frac{-1}{x^2} = 0$ for $x=0$.
8659
How do you show that $e^{-1/x^2}$ is differentiable at $0$?
138559
How can I show that $\frac{1}{1+|z|^2}$ isn't analytic at $z=1$?
13612
Show the existence of a complex differentiable function defined outside $|z|=4$ with derivative $\frac{z}{(z-1)(z-2)(z-3)}$
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
49408
Proof of the derivative of ln(x)
46642
Continuity of $\sin(x)/x$
68538
Show that if $ A(t) \in \mathbb{R ^{n×n}}$ is a differentiable function of $t$ then $\frac{d(det A(t))}{dt}$
34081
Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
98462
Prove the inverse of a strictly increasing function is differentiable.
71094
Proof that 1-1 analytic functions have nonzero derivative