Proving a function is smooth, and has derivatives of all orders at 0
136195
Stuck trying to prove that $e^{-x^{-2}}$ is $C^{\infty}$
97371
Proving a function is constant, under certain conditions?
57180
Techniques to prove a function is uniformly continuous
16291
Discontinuous derivative.
111470
Proof of differentiability of $f(x)$
43956
Differentiating $f(x)^{g(x)}$
69378
The derivative of $x!$ and its continuity
53767
How to prove that derivatives have the Intermediate Value Property
146318
Derivative of f(x)=arth(lnx)
131444
Local maximum implies derivative is $0$
26388
proof that function is constant
150833
Discontinuities of the derivative of a differentiable function on closed interval
104263
How to show that $f'(x)<2f(x)$
85157
Does a smooth "transition function" with bounded derivatives exist?
158407
derivative bounded by a constant multiple of the function
71260
Check differentiability of multivariable functions
105068
Proving that the function is differentiable and $f'(0)=0$