Site - Johny Carvalho: Física, Matemática e Telecomunicações
1.0 - Limites Fundamentais
Fundamental Limits
\(\lim \limits_{x\to\,0} \dfrac{\sin(x)}{x}=1\) \(\lim \limits_{x\to\,0} \dfrac{\cos(x)-1}{x}=0\)
  
\(\lim \limits_{x\to\,\pm\infty} \left(1+ \dfrac{1}{x}\right)^x=e\) \(\lim \limits_{x\to\,0} \dfrac{a^x - 1}{x}=\ln a\)

2.0 - Derivada das Funções Trigonométricas
Derivative of Trigonometric Functions

\(\dfrac{d}{dx}\sin(x)=\cos(x)\)

\(\dfrac{d}{dx}\cos(x)=-\sin(x)\)

\(\dfrac{d}{dx}\tan(x)=\sec^2(x)\)

\(\dfrac{d}{dx}\cot(x)=-\csc^2(x)\)

\(\dfrac{d}{dx}\sec(x)=\sec(x)\tan(x)\)

\(\dfrac{d}{dx}\csc(x)=-\csc(x)\cot(x)\)

3.0 - Derivada das Funções Trigonométricas Inversas
Derivative of Inverse Trigonometric Functions

\(\dfrac{d}{du}\sin^{-1}(u)=\dfrac{1}{\sqrt{1-u^2}}\)

\(\dfrac{d}{du}\cos^{-1}(u)=-\dfrac{1}{\sqrt{1-u^2}}\)

\(\dfrac{d}{du}\tan^{-1}(u)=\dfrac{1}{1+u^2}\)

\(\dfrac{d}{du}\cot^{-1}(u)=-\dfrac{1}{1+u^2}\)

\(\dfrac{d}{du}\sec^{-1}(u)=\dfrac{1}{|u|\sqrt{u^2-1}} \)

\(\dfrac{d}{du}\csc^{-1}(u)=-\dfrac{1}{|u|\sqrt{u^2-1}} \)