If $y = \sqrt{x + \sqrt{x+\sqrt{x+\ldots}}}$ prove that $\frac{dy}{dx}=\frac{1}{2y-1}$
61293
What's the derivative of: $ \sqrt{x+\sqrt{{x}+\sqrt{x+\cdots}}}$?
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
11707
If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$
129171
Prove that $1+\frac{1}{3}+\frac{1\cdot 3}{3\cdot 6}+\frac{1\cdot 3\cdot 5}{3\cdot 6 \cdot 9}+.........=\sqrt{3}$
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
99930
Find the Maximum value of $\frac{x}{\sqrt{x+y}}+\frac{y}{\sqrt{y+z}}+\frac{z}{\sqrt{z+x}}$
822
Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$
11289
Why $d(x) + d(y) \le n$ when proving Mantel's theorem
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
3406
Prove that $\frac{\partial x}{\partial y} \frac{\partial y}{\partial z} \frac{\partial z}{\partial x} = -1$ and verify ideal gas law
26876
How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$?
18016
Proof of the following inequality $ \frac{x - y}{\log x - \log y} > \sqrt{xy} $, $x>y$.
25203
with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
77464
Prove that ${x dy - y d x\over x^2 + y^2}$ is not exact
34349
Prove that $\frac{1}{1+x_1}+\frac{1}{1+x_2}+\cdots+\frac{1}{1+x_n} \geq \frac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$
81437
Find the value of $y(1)$ of the ODE $y'+y=|x|$.
52427
Prove, $\sqrt{n} \le (n!)^\frac{1}{n} \le \frac{n+1}{2} $