DERIVADAS FORMULAS

𝑦 = 𝑘 𝑦′ = 0 𝑦 = 𝑢 + 𝑣 𝑦 = 𝑢 + 𝑣′ 𝑦 = 𝑢 ∙ 𝑣 𝑦 = 𝑢 𝑣 + 𝑢𝑣′ 𝑦 = 𝑘𝑥 𝑦′ = 𝑘 𝑦 = 𝑢 − 𝑣 𝑦 = 𝑢 − 𝑣′ 𝑦 = 𝑢 𝑣⁄ 𝑦 = 𝑢 𝑣 − 𝑢𝑣 𝑣

Tipo potencial

axy = 1−=′ aaxy

Tipo raíz cuadrada

xy = x

y2

1=′

afy = fafy a ′=′ − .1 fy = ffy

2′

=′

Tipo exponencial

xey = xey =′

Tipo logarítmico

Lxy = x

y 1=′

fey = fey f ′= . Lfy = ffy′

=′

xay = Laay x .= xy alog= Lax

y 1.1=′

fay = Lafay f .. ′= fy alog= Laf

fy 1.′

=′

Tipo seno

senxy = xy cos=′

Tipo cosecante

ecxy cos= .gxcotecxcosy ⋅−=′

senfy = ffy ′=′ .cos ecfy cos= ( ) ( ).fgcotfeccosfy ⋅⋅′−=′

Tipo coseno

xy cos= senxy −=′

Tipo secante

xy sec= .tgxxsecy ⋅=′

fy cos=

fsenfy ′−=′ . fy sec= ( ) ( ).ftgfsecfy ⋅⋅′=′

Tipo tangente

tgxy = xtgx

y 22 1

cos1

+==′ Tipo cotangente

ctgxy = xsen

y 2

1−=′

tgfy = ff

y ′=′ .cos

12

ctgfy = ffsen

y ′−=′ .1

2

Funciones arco

arcsenxy = 21

1

xy

−=′ arcsenfy = f

fy ′

−=′ .

1

12

xy arccos=

21

1

xy

−

−=′ fy arccos= f

fy ′

−

−=′ .

1

12

arctgxy =

21

1x

y+

=′ arctgfy = ff

y ′+

=′ .1

12

xarcy sec= .1xx

1y2 −⋅

=′ ( )farcy sec= ( ).

1ff

fy2 −⋅

′=′

ecxy arccos=

.1xx

1y2 −⋅

−=′ ( )fecy arccos= ( )

.1ff

fy2 −⋅

′−=′

gxarcy cot= .x11y2+

−=′ ( )fgarcy cot= ( )

.f1fy2+

′−=′

derivadas

𝑦 = 𝑘 𝑦′ = 0 𝑦 = 𝑢 + 𝑣 𝑦 = 𝑢 + 𝑣′ 𝑦 = 𝑢 ∙ 𝑣 𝑦 = 𝑢 𝑣 + 𝑢𝑣′ 𝑦 = 𝑘𝑥 𝑦′ = 𝑘 𝑦 = 𝑢 − 𝑣 𝑦 = 𝑢 − 𝑣′ 𝑦 = 𝑢 𝑣⁄ 𝑦 = 𝑢 𝑣 − 𝑢𝑣 𝑣

Tipo potencial

axy = 1−=′ aaxy

Tipo raíz cuadrada

xy = x

y2

1=′

afy = fafy a ′=′ − .1 fy = ffy

2′

=′

Tipo exponencial

xey = xey =′

Tipo logarítmico

Lxy = x

y 1=′

fey = fey f ′= . Lfy = ffy′

=′

xay = Laay x .= xy alog= Lax

y 1.1=′

fay = Lafay f .. ′= fy alog= Laf

fy 1.′

=′

Tipo seno

senxy = xy cos=′

Tipo cosecante

ecxy cos= .gxcotecxcosy ⋅−=′

senfy = ffy ′=′ .cos ecfy cos= ( ) ( ).fgcotfeccosfy ⋅⋅′−=′

Tipo coseno

xy cos= senxy −=′

Tipo secante

xy sec= .tgxxsecy ⋅=′

fy cos=

fsenfy ′−=′ . fy sec= ( ) ( ).ftgfsecfy ⋅⋅′=′

Tipo tangente

tgxy = xtgx

y 22 1

cos1

+==′ Tipo cotangente

ctgxy = xsen

y 2

1−=′

tgfy = ff

y ′=′ .cos

12

ctgfy = ffsen

y ′−=′ .1

2

Funciones arco

arcsenxy = 21

1

xy

−=′ arcsenfy = f

fy ′

−=′ .

1

12

xy arccos=

21

1

xy

−

−=′ fy arccos= f

fy ′

−

−=′ .

1

12

arctgxy =

21

1x

y+

=′ arctgfy = ff

y ′+

=′ .1

12

xarcy sec= .1xx

1y2 −⋅

=′ ( )farcy sec= ( ).

1ff

fy2 −⋅

′=′

ecxy arccos=

.1xx

1y2 −⋅

−=′ ( )fecy arccos= ( )

.1ff

fy2 −⋅

′−=′

gxarcy cot= .x11y2+

−=′ ( )fgarcy cot= ( )

.f1fy2+

′−=′

derivadas