NutShell of a Peanut

$T=2\pi {\sqrt {\frac {L}{g}}}$

$f(x)=x^{2}$ $f'(x)=2x$ $\int \,2x\,dx=x^{2}=\int \,f'(x)\,dx=f(x)$

$\sum _{k=0}^{n}{\binom {n}{k}}a^{n-k}b^{k}$ ${\binom {n}{k}}={\frac {n!}{k!(n-k)!}}$ $(a+b)^{n}$

$x^{2}+y^{2}=r^{2}$

${\frac {x^{2}}{r^{2}}}+{\frac {y^{2}}{r^{2}}}=1$ Circle

${\frac {x^{2}}{a_{s}}}+{\frac {y^{2}}{b_{l}}}=1$

$\int _{x_{1}}^{x_{2}}\,{\frac {x^{2}}{r^{2}}}+{\frac {y^{2}}{r^{2}}}\,dx$ Area of circle

$\oint _{x_{1}}^{x_{2}}\,{\frac {x^{2}}{r^{2}}}+{\frac {y^{2}}{r^{2}}}\,dx\,$ Circumference of circle

$G_{\mu \nu }+{\Lambda g}_{\mu \nu }={\frac {8\pi G}{c^{4}}}T_{\mu \nu }$

$F_{g}=G{\frac {m_{1}m_{2}}{r^{2}}}$

Story of the 3 forts

${\frac {3}{4}}\,t_{p}-t_{e}=t_{past}\,{\frac {F^{3}}{R^{h}}}$

$\oint _{4}^{3}\,P=LW$ $\times$ $\aleph _{0}^{army}>\infty$

$\psi \longrightarrow \forall \in C|\exists$

The End

${\frac {d}{dx}}[{\frac {x^{n+1}}{n+1}}+C]=x^{n}$ $\int x^{n}\,dx={\frac {x^{n+1}}{n+1}}+C$

$\sum _{i=1}^{n}(x_{i-1})\Delta {x}$

$\int _{b}^{a}\,f(x)\,dx=\sum _{R=1}^{R}A_{R}$

${\frac {d}{dx}}e^{x}=e^{x}$ $\int e^{x}\,dx=e^{x}$

$E_{k}={\frac {1}{2}}mv^{2}$

$p=mv$

${\frac {p}{m}}=v$

$E={\frac {1}{2}}m({\frac {p}{m}})({\frac {p}{m}})$

$E={\frac {1}{2}}m({\frac {p^{2}}{m^{2}}})$

$E={\frac {p^{2}}{2m}}$

${\frac {d}{dx}}\pi {r^{2}}=2\pi {r}$

$\int 2\pi {r}\,dx=\pi {r^{2}}$

Sphere

${\frac {d}{dx}}{\frac {4}{3}}\pi {r^{3}}=4\pi {r^{2}}$

$\int 4\pi {r^{2}}dx={\frac {4}{3}}\pi {r^{3}}$ $\int {\frac {d}{dx}}f(x)dx=f(x)$

$f(x,y)=x^{2}sin(y)$

${\frac {\partial f}{\partial x}}=2sin(y)x$

${\frac {\partial f}{\partial y}}=x^{2}cos(y)$

$\nabla f={\frac {\partial f}{\partial x}},{\frac {\partial f}{\partial y}}$