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