Proving $\frac {\partial ^2 f}{\partial x\, \partial y} = \frac {\partial ^2 f}{\partial y \,\partial x}$ by the derivative theorem
53640
Equality of mixed partial derivatives
155333
Prove that $\lim_{x\to\infty}\frac{f(x)}x=\lim_{x\to\infty}f'(x)$
78834
if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $
40549
How to proof the the derivative of $x^2$ is $2x$?
129394
understanding $\frac{\partial x}{\partial y}\frac{\partial y}{\partial z}\frac{\partial z}{\partial x}=-1$
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
12375
Prove $\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$
87613
Infinitely differentiable functions: how to prove that $e^\frac{1}{x^2-1}$ has derivative of any order?
145496
Show $\lim_{h \to \ 0} \frac{f(x + 2h) - 2f(x+h) + f(x)}{h^{2}} = f''(x)$ Proof verification
147299
Prove that $g(x,y) = \frac{x^3y}{x^2+y^2}$ with $g(0,0)=0$ is continuous
44880
Prove that the derivative of an even differentiable function is odd, and the derivative of an odd is even.
95774
$\frac{\partial^2 u}{\partial t^2}-c^2\frac{\partial^2u}{\partial x^2}=0\text{ implies } \frac{\partial^2 u}{\partial z \partial y}=0$
34081
Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
64437
Proof by induction (power rule of the derivative)
107290
proof of product rule of derivatives using first principle?
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
152895
What is wrong with this derivation of $\frac{d}{dx}x^2$?