Prove that the derivative of an even differentiable function is odd, and the derivative of an odd differentiable function is even.
15155
Derivative of an even function is odd and vice versa
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
105084
Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
15287
Proving that second derivative is perpendicular to curve
74583
Prove that $f'(0)=L$.
30533
Showing that this function is infinitely differentiable
144713
Simple Calculus Proof
93967
Prove partial derivatives exist, but not all directional derivatives exists.
154288
proof that Even powers of an odd function's taylor polynomial vanish
75653
Prove that $|f ''|\ge 4$
138864
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f(x+y)=f(x)f(y)$ and $f'(0)$ exists, then $f$ is differentiable on $\mathbb R$
111458
Prove that $f$ is differentiable
78834
if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $
105319
A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$
116056
Prove that $|f(x)-f(y)|\le|x-y|$ for all $x$ and $y$.
154471
Prove that the Riemann zeta function has all higher order derivatives.
18734
Showing that a function is differentiable