Tabela de derivadas

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Regras de Diferenciação
d (c ) = 0 dx

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d [c f (x )] = c f ' (x ) dx d [f (x ) + g(x )] = f ' (x ) + g' (x ) dx
d [f (x ) − g(x)] = f ' (x ) − g ' (x ) dx d [f (x ) g(x )] = f ' (x ) g(x ) + f (x ) g' (x ) dx

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d 1 arc sen ( x ) = dx 1− x2 d 1 arc cos( x ) = − dx 1−x2
d 1 arc tg ( x ) = dx 1+ x2 d 1 arc cos sec( x ) = − dx x x2 −1 d 1 arc sec( x ) = dx x x 2 −1 d 1 arc cot g ( x ) = − dx 1+ x2 d senh ( x ) =cosh( x ) dx d cosh( x ) = senh ( x ) dx d tgh ( x ) = sec h 2 ( x ) dx d cos sec h ( x ) = − cos sec h ( x ) cot gh ( x ) dx d sec h ( x ) = −sec h ( x ) tgh ( x ) dx

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d  f (x )  f ' (x ) g(x ) − f (x ) g' (x ) = dx  g(x )  [g(x )]2  
d f (g (x )) = f ' (g ( x )) g ' ( x ) dx d n ( x ) = n x n −1 dx d x (e ) = e x dx d x (a ) = a x ln(a ) dx d 1 ln x = dx x

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d 1 log a ( x ) = dx x ln(a ) d sen ( x ) = cos( x ) dx d cos( x ) = −sen ( x ) dx d tg ( x ) = sec 2 ( x) dx d cos sec( x ) = − cos sec( x ) cot( x ) dx
d sec( x ) = sec( x ) tg ( x ) dx d cot g ( x ) = − cos sec2 ( x ) dx

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d cot gh ( x ) =− cos sec h 2 ( x ) dx d 1 arc senh ( x ) = dx 1+ x2 d 1 arc cosh( x ) = dx x 2 −1 d 1 arc tgh ( x ) = dx 1− x2 d 1 arc cos sec h ( x ) = − dx x x2+1
d 1 arc sec h ( x ) = − dx x 1− x2 d 1 arc cot gh ( x ) = dx 1− x2

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