Is there a proof for $\frac{\mathrm{d}y}{\mathrm{d}x} = - \frac{\frac{\partial }{\partial x}}{\frac{\partial }{\partial y}}$?
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
85076
Is it true that $d(x,Y)=d(x,y_0)$ for some $y_0 \in Y$ when $Y$ is closed?
146594
Prove that $\frac{d}{dx}(\tan^{-1}(x))=\frac{1}{1+x^2}dx$
83531
Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $
120985
Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
152895
What is wrong with this derivation of $\frac{d}{dx}x^2$?
20280
Proving that expression is equivalent to the definition of derivative
136782
Prove that $x * y = \frac{x+y}{1+xy}$ is a stable part of $G=(-1, 1)$
68097
Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$
150417
Two apparently different antiderivatives of $\frac{1}{2 x}$
86567
Understanding $\sum_{x = 0}^y x = \frac{y(y + 1)}{2}$ in a step of a proof
68538
Show that if $ A(t) \in \mathbb{R ^{n×n}}$ is a differentiable function of $t$ then $\frac{d(det A(t))}{dt}$
71708
Proving that $\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) \lvert f(z) \rvert^2 = 4 \lvert f'(z) \rvert^2$
62055
Solve $\frac{d}{dx}f(x)=f(x-1)$
98454
Prove that, $\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}\ge 4$ where we do not use AM-GM inequality on the given statement to prove it.
115712
Application of Derivatives rigorous proof
108808
$x =r\cos \theta$ and $y = r\sin\theta$, determine $\frac{\partial r}{\partial x}$ and $\frac{\partial \theta}{\partial x}$