Let $f(x) := x^2 \sin \frac 1 x, f(0)=0$. Show $f$ is differentiable on $\mathbb R$.
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
57407
Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.
68538
Show that if $ A(t) \in \mathbb{R ^{n×n}}$ is a differentiable function of $t$ then $\frac{d(det A(t))}{dt}$
28399
Showing $f$ is constant
149764
If $f$ s twice differentiable and satisfies the following constraints, prove $f'(0)>-\sqrt 2$
49705
Is $f(x,y)=(x+2y+y^2+|xy|, 2x+y+x^2+|xy|)$ differentiable?
99795
Derivative of piece-wise function given by $x\sin\frac1x$ at $x=0$
138864
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f(x+y)=f(x)f(y)$ and $f'(0)$ exists, then $f$ is differentiable on $\mathbb R$
67020
Proving that for a smooth function if $f(\frac 1 k)=0 :\forall k\in \mathbb N$ then $f(x)=0 :\forall x\in[-1,1]$
68048
Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$
30855
Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.
106013
Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable
131357
Prove that $f(x,y)=xy$ is differentiable using the definition
142490
Alternative proof for differentiability of inverse function?
27888
Why is $|x|$ not differentiable at $x=0$?
111470
Proof of differentiability of $f(x)$
78834
if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $