Is $f(x)=e^x$ the only solution to $f(f'(x))=f'(f(x))$?
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
99906
If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
64339
Find $f$ where $f'(x) = f(1+x)$
124581
Solving $x^2 - 1 = e^x$
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
27646
Why do we chose exponential function as a trial solution for second order linear differential equation with constant coefficient?
131424
which of the following is NOT a possible value of $(e^{f})''(0)$??
148556
Could you explain why $\frac{d}{dx} e^x = e^x$ "intuitively"?
74583
Prove that $f'(0)=L$.
21954
A question about $f(x)\equiv 0$
20568
Does the following have a solution for f(x,y)?
114307
Are Exponential and Trigonometric Functions the Only Non-Trivial Solutions to $F'(x)=F(x+a)$?
130322
Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$