Tecnicas de derivação
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Lista1_DerivadasTécnicas de Derivação – Uso da Tabelada de Derivadas Propriedades da Derivação
h) g ( x ) = x 2 ⋅ 3 x 3 − 1
(
)
2
g ' ( x) = 15 x 4 − 2 x
y = c → y' = 0 y = c u → y' = c u' y = u ± v → y ' = u ' ± v' y = u ⋅ v → y ' = u ' ⋅ v + v' ⋅ u u u '⋅v − v'⋅u y = → y' = v v2
1) Utilizando as Regras de Derivação indicadas, observe as operações entre as funções para usar a propriedade indicada e determine a derivada de cada função.
i) f ( x) = x 2 + 3x x 3 − 9 x
)( j ) f ( x) = (2 x − 1)(4 x
1 3x − 2 2+ x 3− x 2x + 7 3x − 1
(
) + 7)
f ' ( x) = 5 x 4 + 12 x 3 − 27 x 2 − 54 x
k ) f ( x) = l ) f ( x) =
m) f ( x ) =
f ' ( x) = 24 x 2 − 8 x + 14 −3 f ' ( x) = (3x − 2)2 5 f ' ( x) = (3 − x )2 − 23 f ' ( x) = (3x − 1)2 f ' ( x) = − 10 18 1 − − +3 x6 x4 x2
1 2 n) f ( x) = 2 + 3 3 + x x x
II) y = c u k → y ' = c ku k −1 ⋅ u '
I) y = c x n → y ' = c nx n−1
a) f ( x) = x 5 − 3 x 3 + 1 x10 x 5 b) f ( x ) = + +6 2 5 3 4 c ) f ( x) = 2 + x x 5 25 d ) h( y ) = 5 − y y e) g ( x) = 3 x − 2 − 7 x −1 + 6 2 2 f ) f ( x) = − 2 5 x 3x g ) g ( x) = 3 ⋅ x 3 − x 2 f ' ( x) = 5 x 4 − 9 x 2 f ' ( x) = 5 x + x f ' ( x) = −
9 4
(
)
6 4 − 2 3 x x 25 25 h' ( y ) = − 6 + 2 y y 6 7 g ' ( x) = − 3 + 2 x x 2 2 2 f ' ( x) = − 2 + 3 5x 3x 2 g ' ( x) = 3 ⋅ 3x − 2 x
( ) b) g ( x) = (4 x + 3) c) f ( x) = (x + 2 ) d ) f ( x) = (x + 4 x − 5) e)h( x) = (3x + 7 ) (5 − 3 x ) a ) f ( x) = 6 x 2 + 7
2 2 2 3 15 2 3 2 2
f ' ( x) = 144 x 3 + 168 x g ' ( x) = 64 x 3 + 48 x f ' ( x) = 45 x 2 x 3 + 2
(
)
14 2
f ' ( x) = (6 x + 12) x 2 + 4 x − 5 g ' ( x) = 3 x 2
4
3
(
( ) + 7 )(5 − 3x ) (− 63x
2 −3 3 2
2
+ 60 x − 63
)
f ) f ( x) = (7 x + 3)
−2 3
(2 x − 1)
f ' ( x) = (7 x + 3) g ' ( x) =
(2 x − 1) (28 x + 38)
3x + 1 g ) g ( x) = 2 x
(3x + 1)
( −9 x − 6) x7
(
)
1/4
UNIVERSIDADE DE UBERABA CURSOS DE ENGENHARIAS E TECNOLOGIAS Estudos Lógicos