Differentiability of $f(x) = \exp(-1/x^2), f(0) = 0$
8659
How do you show that $e^{-1/x^2}$ is differentiable at $0$?
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 $(0,1)$
59911
Looking for help with a proof that n-th derivative of $e^\frac{-1}{x^2} = 0$ for $x=0$.
107254
Real analysis question $e^{-1/x^2}$
25467
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
43956
Differentiating $f(x)^{g(x)}$
34136
$f$ is differentiable in $[0,1]$ ,$\sup_{x\in[0,1]}|f'(x)| \le M\lt+\infty $
57695
Show $\inf_f\int_0^1|f'(x)-f(x)|dx=1/e$ for continuously differentiable functions with $f(0)=0$, $f(1)=1$.
86860
Continuity of differentiable function $x^2\sin(1/x)$
97146
differentiate with respect to a function
70830
How to evaluate $\int_{0}^{\infty}\exp(-x^2-1/x^2)dx$?
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
30860
Prove that $f(x)=0$ in $[-1,1]$.
113888
Behavior of derivative near the zero of a function.
85623
Proof of continuity implied by differentiability
120784
Differentiablility over closed intervals