Prove the differentiability of funtion $f(x)$ using the condition of $\lim\limits_{x\to0}\frac{f(x)-f(ax)}{x}=A$.
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
115635
Differentiability of antiderivative and continuity of derivative
131357
Prove that $f(x,y)=xy$ is differentiable using the definition
68538
Show that if $ A(t) \in \mathbb{R ^{n×n}}$ is a differentiable function of $t$ then $\frac{d(det A(t))}{dt}$
142870
Prove the function is not differentiable at (0,0)
38923
What can we say about differentiability of $f$ at $c$?
34187
The limit of the derivative of an increasing and bounded function is always $0$?
158681
How to show that $e^x$ is differentiable?
115712
Application of Derivatives rigorous proof
126256
Prove limit of function
60321
Use the definition of derivative to prove $\lim_{x\to 0}\ln(x+1)/x =1$
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
83707
Suppose that $f$ is differentiable on $\mathbb{R}$ and $\lim_{x\to \infty}f'(x)=M$. Show that $\lim_{x\to \infty}f(x+1)-f(x)$ exists and find it.
44129
If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$.
127114
Differentiability implying continuity
121217
How to show that $\lim\limits_{x \to \infty} f'(x) = 0$ implies $\lim\limits_{x \to \infty} \frac{f(x)}{x} = 0$?