Formulas de Derivadas de Funciones Trigonométricas

Formulas de Derivadas de Funciones Trigonométricas
Formulas de la derivada del seno de una función
Formula 1
d
( Sen ⋅ x) = Cos ⋅ x
dx
Formula 2
d
d
( Sen ⋅ u ) = Cos ⋅ u ⋅ u
dx
dx
Formula 3
d
d
( Sen m ⋅ u ) = mSen m−1u ⋅ Cos ⋅ u ⋅ u
dx
dx
Formulas de la derivada del coseno de una función
Formula 1
d
(Cos ⋅ x ) = − Sen ⋅ x
dx
Formula 2
d
d
(Cos ⋅ u ) = − Sen ⋅ u ⋅ u
dx
dx
Formula 3
d
d
(Cos m ⋅ u ) = −mCos m−1u ⋅ Sen ⋅ u ⋅ u
dx
dx
Formulas de la derivada de la tangente de una función
Formula 1
d
(tan⋅ x) = Sec 2 ⋅ x
dx
Formula 2
d
d
(tan⋅ u ) = Sec 2 ⋅ u ⋅ u
dx
dx
Formula 3
d
d
(tan m ⋅ u ) = m tan m−1 u ⋅ Sec 2 u u
dx
dx
Formulas de la derivada de la Cotangente de una función
Formula 1
Formula 2
d
(Cot ⋅ x) = −Csc 2 ⋅ x
dx
d
d
(Cot ⋅ u ) = −Csc 2 ⋅ u ⋅ u
dx
dx
Formula 3
d
d
(Cot m ⋅ u ) = −mCot m −1u ⋅ Csc 2u u
dx
dx
Formulas de la derivada de la Secante de una función
Formula 1
Formula 2
d
( Sec ⋅ x) = tan⋅ x ⋅ Sec ⋅ x
dx
d
d
( Sec ⋅ u ) = tan⋅ u ⋅ Sec ⋅ u u
dx
dx
Formula 3
d
d
( Sec m ⋅ u ) = mSec mu ⋅ tan⋅ u u
dx
dx
Formulas de la derivada de la Cosecante de una función
Formula 1
Formula 2
d
(Csc ⋅ x) = −Cot ⋅ x ⋅ Csc ⋅ x
dx
d
d
(Csc ⋅ u ) = −Cot ⋅ u ⋅ Csc ⋅ u u
dx
dx
Formula 3
d
d
(Csc m ⋅ u ) = −mCsc mu ⋅ Cot ⋅ u u
dx
dx
Formulas de Derivadas de Funciones Trigonométricas Inversas
du
d
( arc ⋅ Sen ⋅ u ) = dx 2
dx
1− u
arc ⋅ Sen ⋅ x = sen −1 x
du
d
( arc ⋅ Cos ⋅ u ) = − dx 2
dx
1− u
du
d
(arc ⋅ tan⋅ u ) = dx 2
dx
1+ u
du
d
(arc ⋅ Cot ⋅ u ) = − dx 2
dx
1+ u
du
d
dx
(arc ⋅ Sec ⋅ u ) =
dx
u u2 −1
du
d
(arc ⋅ Csc ⋅ u ) = − dx2
dx
u u −1
Derivadas de Funciones Logarítmicas y Exponenciales
d
log a e du
log a u =
⋅
dx
u
dx
para a ≠ 0,1
d
d
1 d
ln u = log e u =
u
dx
dx
u dx
d u
d
a = a u ln a u
dx
dx
d u
d
e = eu u
dx
dx
d v d v ln u
d
du
dv
u = e
= ev ln u [v ln u ] = vu v −1
+ u v ln u
dx
dx
dx
dx
dx