Show $\bigg(\frac{\partial x}{\partial y}\bigg) \bigg(\frac{\partial y}{\partial z}\bigg)\bigg(\frac{\partial z}{\partial x}\bigg) = - 1,$
3406
Prove that $\frac{\partial x}{\partial y} \frac{\partial y}{\partial z} \frac{\partial z}{\partial x} = -1$ and verify ideal gas law
39995
Showing that partial derivatives of $f(x) = \frac{xy}{x^2+y^2}$ exist for $(x,y) \neq (0,0)$
96112
Differentiating $ \left( 1 - \frac {1}{x} \right)^x $
99676
Prove $\sum{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$
146594
Prove that $\frac{d}{dx}(\tan^{-1}(x))=\frac{1}{1+x^2}dx$
80553
Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
95774
$\frac{\partial^2 u}{\partial t^2}-c^2\frac{\partial^2u}{\partial x^2}=0\text{ implies } \frac{\partial^2 u}{\partial z \partial y}=0$
85984
How come $\frac{\partial(\partial_{\beta}A_{\gamma})}{\partial(\partial_{\mu}A_{\nu})} = g_{\beta\mu}g_{\gamma\nu}$?
151297
Second order partial of $f(x,y)=\frac{xy(x^2-y^2)}{x^2+y^2}$
138107
Showing that $\left|\frac{z-a}{1-\bar{a}z}\right|=1$
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
72906
Is $\frac{\partial}{\partial x_1}=\frac{\partial}{\partial y_1}$ if $x_1=y_1$?
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
16774
If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.
136782
Prove that $x * y = \frac{x+y}{1+xy}$ is a stable part of $G=(-1, 1)$
15104
Show that $\big|\frac{a-b}{1-\overline{a}b}\big|=1$, when either $|a|=1$ or $|b|=1$.
123674
Show that $y = \frac{2x}{x^2 +1}$ lies between $-1$ and $1$ inclusive.