If $\lim_{x \rightarrow 1} f'(x)=2015$. Prove that $f$ is differentiable at $x=1$.
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
119907
Finding the Derivative of |x| using the Limit Definition
57407
Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
55125
Continuous right derivative implies differentiability
60321
Use the definition of derivative to prove $\lim_{x\to 0}\ln(x+1)/x =1$
151958
How to show $f'(0)$ exist and is equal to $1$?
143874
Limit of derivative is zero. Does it imply a limit for f(x)?
40487
Given $\lim_{x \rightarrow a}f(x)+\frac1{\left|f(x)\right|}=0$, what is $\lim_{x \rightarrow a}f(x)$?
158681
How to show that $e^x$ is differentiable?
58943
If $f'(x)\le g'(x)$, prove $f(x)\le g(x)$
41434
Show that: $\lim \limits_{n \rightarrow+\infty} \int_{0}^{1}{f(x^n)dx}=f(0)$
145233
How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?
99906
If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
68048
Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$