On proving that $f(x) = f'(x)\iff f(x) = e^x$. (Not aware of a possible duplicate.)
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
43733
$|f'(x)| \le g(x)$ implies $|f(b) - f(a)| \le \int_a^b g(x) dx$, without assuming $f'$ to be integrable.
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
58943
If $f'(x)\le g'(x)$, prove $f(x)\le g(x)$
71857
Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $
148556
Could you explain why $\frac{d}{dx} e^x = e^x$ "intuitively"?
116056
Prove that $|f(x)-f(y)|\le|x-y|$ for all $x$ and $y$.
111470
Proof of differentiability of $f(x)$
145496
Show $\lim_{h \to \ 0} \frac{f(x + 2h) - 2f(x+h) + f(x)}{h^{2}} = f''(x)$ Proof verification
135693
Suppose f is a twice differentiable function with $f(0)=0$ and $f(1)=1$, $f'(0)=f'(1)=0$. Then show that $|f''(x)| > 4$ for some $x$ in $(0,1)$
109561
Find $F'(x)$ if $F(x) = \displaystyle \int_{0}^x xf(t)dt$.
122481
proof of an identity for exponential function
60348
How do I prove $F(a)=F(a^2)?$
57026
$f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
128495
Integral Inequality $|f''(x)/f(x)|$
114747
If $\lim_{x \to \infty}f'(x)=+\infty$ then $\lim_{x \to \infty}(f(x)-f(x-1))=+\infty$ and $\lim_{x \to \infty}f(x)=+\infty$.
65054
How is $e^z$ the only function that is entire with the property $f'(z) = f(z)$ and $f(0) = 1$