Tabla Derivadas
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Centro «Sta. María de la Capilla» – HH. Maristas – – Jaén – Tabla de derivadas Tipo de función Función Derivada Suma y = f + g y = f + g Resta y = f − g y = f − g Producto y = f ⋅ g y = f ⋅ g + g ⋅ f Cociente (Prop. Inversa) y = f g y = f ⋅ g − g ⋅ f g 2 Operaciones Radical y = f n y = f n ⋅ ( f ) n −1 n y = a (a = cte) y = 0 y = a⋅ x n y = n⋅ a⋅ x n -1 Polinómica y = ( f ) n y = n ⋅ ( f ) n −1 ⋅ f y = Ln(x) y = 1 x y = Ln f () y = f f y = log a ( x ) y = 1 x ⋅ log a e Logarítmica y = log a f ( ) y = f f ⋅ log a e y = a x y = a x ⋅ Ln( a) y = a f y = f ⋅ a f ⋅ Ln( a) y = e x y = e x Exponencial y = e f y = f ⋅ e f y = senx y = cos x y = sen f ( ) y = f ⋅ cos f ( ) y = sen n f ( ) y = n⋅ sen n −1 f ()⋅ f ⋅ cos f () y = cosx y = −senx y = cos f ( ) y = - f ⋅ sen f () y = cos n f ( ) y = −n⋅ cos n −1 f ( )⋅ f ⋅ sen f ( ) y = tgx y = 1 cos 2 x = 1 + tg 2 x y = tg f ( ) y = f cos 2 f ( ) = f ⋅ 1 + tg 2 f ( ) [ ] Trigonométricas y = tg n f ( ) y = n⋅ tg n −1 f ( )⋅ f cos 2 f ( )
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Tabla de derivadas
Transcript of Tabla Derivadas
Centro «Sta. María de la Capilla»
– HH. Maristas – – Jaén –
Tabla de derivadas
Tipo de función Función Derivada Suma
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y = f + g
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ʹ′ y = ʹ′ f + ʹ′ g Resta
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y = f − g
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ʹ′ y = ʹ′ f − ʹ′ g Producto
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y = f ⋅ g
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ʹ′ y = ʹ′ f ⋅ g + ʹ′ g ⋅ f
Cociente (Prop. Inversa)
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y =fg
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ʹ′ y =ʹ′ f ⋅ g − ʹ′ g ⋅ f
g2 Operaciones
Radical
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y = fn
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ʹ′ y =ʹ′ f
n⋅ ( f )n−1n
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y = a (a = cte)
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ʹ′ y = 0
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y = a⋅ xn
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ʹ′ y = n⋅ a⋅ xn -1 Polinómica
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y = ( f )n
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ʹ′ y = n⋅ ( f )n−1⋅ ʹ′ f
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y = Ln(x)
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ʹ′ y =1x
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y = Ln f( )
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ʹ′ y =ʹ′ f
f
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y = loga (x)
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ʹ′ y =1x⋅ loga e
Logarítmica
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y = loga f( )
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ʹ′ y =ʹ′ f
f⋅ loga e
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y = ax
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ʹ′ y = ax ⋅ Ln(a)
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y = a f
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ʹ′ y = ʹ′ f ⋅ a f ⋅ Ln(a)
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y = ex
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ʹ′ y = ex Exponencial
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y = e f
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ʹ′ y = ʹ′ f ⋅ e f
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y = senx
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ʹ′ y = cos x
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y = sen f( )
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ʹ′ y = ʹ′ f ⋅ cos f( )
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y = senn f( )
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ʹ′ y = n⋅ senn−1 f( )⋅ ʹ′ f ⋅ cos f( )
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y = cosx
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ʹ′ y = −senx
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y = cos f( )
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ʹ′ y = - ʹ′ f ⋅ sen f( )
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y = cosn f( )
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ʹ′ y = −n⋅ cosn−1 f( )⋅ ʹ′ f ⋅ sen f( )
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y = tgx
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ʹ′ y =1
cos2 x=1+ tg2x
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y = tg f( )
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ʹ′ y =ʹ′ f
cos2 f( )= ʹ′ f ⋅ 1+ tg2 f( )[ ]
Trigonométricas
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y = tgn f( )
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ʹ′ y = n⋅ tgn−1 f( )⋅ ʹ′ f cos2 f( )
