Tabelas de engenharia/Tabela de derivadas

Tabela de Deriivadas
${d \over dx}c=0$
${d \over dx}x=1$
${d \over dx}cx=c$
${d \over dx}|x|={x \over |x|}=\operatorname {sgn} x,\qquad x\neq 0$
${d \over dx}x^{c}=cx^{c-1}$ where both xc and cxc-1 are defined.
${d \over dx}\left({1 \over x}\right)={d \over dx}\left(x^{-1}\right)=-x^{-2}=-{1 \over x^{2}}$
${d \over dx}\left({1 \over x^{c}}\right)={d \over dx}\left(x^{-c}\right)=-{c \over x^{c+1}}$
${d \over dx}{\sqrt {x}}={d \over dx}x^{1 \over 2}={1 \over 2}x^{-{1 \over 2}}={1 \over 2{\sqrt {x}}}$ x > 0
${d \over dx}c^{x}={c^{x}\ln c}$ c > 0
${d \over dx}e^{x}=e^{x}$
${d \over dx}\log _{c}x={1 \over x\ln c}$ c > 0, $c\neq 1$
${d \over dx}\ln x={1 \over x}$
${d \over dx}\sin x=\cos x$
${d \over dx}\cos x=-\sin x$
${d \over dx}\tan x=\sec ^{2}x$
${d \over dx}\sec x=\tan x\sec x$
${d \over dx}\cot x=-\csc ^{2}x$
${d \over dx}\csc x=-\csc x\cot x$
${d \over dx}\arcsin x={1 \over {\sqrt {1-x^{2}}}}$
${d \over dx}\arccos x={-1 \over {\sqrt {1-x^{2}}}}$
${d \over dx}\arctan x={1 \over 1+x^{2}}$
${d \over dx}\operatorname {arcsec} x={1 \over |x|{\sqrt {x^{2}-1}}}$
${d \over dx}\operatorname {arccot} x={-1 \over 1+x^{2}}$
${d \over dx}\operatorname {arccsc} x={-1 \over |x|{\sqrt {x^{2}-1}}}$
${d \over dx}\sinh x=\cosh x$
${d \over dx}\cosh x=\sinh x$
${d \over dx}\tanh x={\mbox{sech}}^{2}x$
${d \over dx}{\mbox{sech}}x=-\tanh x{\mbox{sech}}x$
${d \over dx}{\mbox{coth}}x=-{\mbox{csch}}^{2}x$
${d \over dx}{\mbox{csch}}x=-{\mbox{coth}}x{\mbox{csch}}x$
${d \over dx}{\mbox{arcsinh}}x={1 \over {\sqrt {x^{2}+1}}}$
${d \over dx}{\mbox{arccosh}}x={1 \over {\sqrt {x^{2}-1}}}$
${d \over dx}{\mbox{arctanh}}x={1 \over 1-x^{2}}$
${d \over dx}{\mbox{arcsech}}x={1 \over x{\sqrt {1-x^{2}}}}$
${d \over dx}{\mbox{arccoth}}x={1 \over 1-x^{2}}$
${d \over dx}{\mbox{arccsch}}x={-1 \over |x|{\sqrt {1+x^{2}}}}$