formulario derivate notevoli

$(c\cdot f(x){)}^{\prime }=c\cdot f^{\prime }(x)$
$(f(x)\pm g(x){)}^{\prime }=f^{\prime }(x)\pm g^{\prime }(x)$
$(f(x)\cdot g(x){)}^{\prime }=f^{\prime }(x)\cdot g(x)+f(x)\cdot g^{\prime }(x)$
$(f(x)\cdot g(x)\cdot h(x){)}^{\prime }=f^{\prime }(x)\cdot g(x)\cdot h(x)+f(x)\cdot g^{\prime }(x)\cdot h(x)+f(x)\cdot g(x)\cdot h^{\prime }(x)$
$(\frac{1}{f(x)}{)}^{\prime }=-\frac{f^{\prime }(x)}{f(x{)}^2}$
$(\frac{f(x)}{g(x)}{)}^{\prime }=\frac{f^{\prime }(x)\cdot g(x)-f(x)\cdot g^{\prime }(x)}{[g(x){]}^2}$
$(f(x{)}^n{)}^{\prime }=n\cdot f(x{)}^{n-1}\cdot f^{\prime }(x)$
$(f[g(x)]{)}^{\prime }=g^{\prime }(x)\cdot f^{\prime }[g(x)]$
$(f(x{)}^{g(x)}{)}^{\prime }=f(x{)}^{g(x)}\cdot [g^{\prime }(x)\cdot ln[f(x)]+g(x)\cdot \frac{f^{\prime }(x)}{f(x)}]$
$(f^{-1}(y){)}^{\prime }=[\frac{1}{f^{\prime }(x)}],x=f^{-1}(y)$

$(c{)}^{\prime }=0$
$(x{)}^{\prime }=1$
$(x^n{)}^{\prime }=n\cdot x^{n-1}$
$(\frac{1}{x}{)}^{\prime }=-\frac{1}{x^2}$
$(\frac{1}{x^n}{)}^{\prime }=\frac{-n}{x^{n+1}}$
$(\sqrt{x}{)}^{\prime }=\frac{1}{2\sqrt{x}}$
$(\sqrt[n]{x}{)}^{\prime }=\frac{1}{n\cdot \sqrt[n]{x^{n-1}}}$
$(e^x{)}^{\prime }=e^x$
$(a^x{)}^{\prime }=a^x\cdot \ln (a)$
$(\ln (|x|){)}^{\prime }=\frac{1}{x}$
$(lo{g}_a(x){)}^{\prime }=\frac{1}{x\cdot ln(a)}$

$(sin(x){)}^{\prime }=cos(x)$
$(cos(x){)}^{\prime }=-sin(x)$
$(tg(x){)}^{\prime }=se{c}^2(x)=\frac{1}{co{s}^2(x)}=1+t{g}^2(x)$
$(cot(x){)}^{\prime }=-cs{c}^2(x)=-\frac{1}{si{n}^2(x)}=-1-co{t}^2(x)$
$(arcsin(x){)}^{\prime }=\frac{1}{\sqrt{1-x^2}}$
$(arccos(x){)}^{\prime }=-\frac{1}{\sqrt{1-x^2}}$
$(arctg(x){)}^{\prime }=\frac{1}{1+x^2}$
$(arccotg(x){)}^{\prime }=-\frac{1}{1+x^2}$

$(csc(x){)}^{\prime }=cot(x)$
$(sec(x){)}^{\prime }=tg(x)$

Seno e coseno iperbolico

$\sinh (x)=\frac{e^x-e^{-x}}{2}$
$\cosh (x)=\frac{e^x+e^{-x}}{2}$

$(\sinh (x){)}^{\prime }=\cosh (x)$
$(\cosh (x){)}^{\prime }=\sinh (x)$

$\int \sinh (x)dx=\cosh (x)+c$
$\int \cosh (x)dx=\sinh (x)+c$

seno e coseno iperbolico