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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