![EJERCICIOS DE DERIVADAS
Hallar las derivadas de las funciones indicadas.
a) G (x) = 2x2 – 5
G’ (x) = 2 . 2x
G’ (x) = 4x
b) Y = (x - 1) (x - 2) (x - 3)
Y = (x2 - 2x – x + 2) (x – 3)
Y = x3 – 3x2 – 2x2 + 6x – x2 + 3x + 2x – 6
Y = x3 – 6x2 + 11x – 6
Y’ = 3x2 - 6. 2x + 11
Y’ = 3x2 – 12x + 11
c) G (x) =
𝟏−𝐜𝐨𝐬 𝒙
𝟏+𝐜𝐨𝐬 𝒙
G’(x) =
(1+cos 𝑥) (1−cos 𝑥)′−(1+cos 𝑥)′ (1−cos 𝑥)
(1+𝑐𝑜𝑠 𝑥)2
=
(1+cos 𝑥) (–( 𝑠𝑒𝑛 𝑥)) −(−𝑠𝑒𝑛 𝑥)(1−cos 𝑥)
(1+𝑐𝑜𝑠 𝑥)2
=
𝑠𝑒𝑛 𝑥 (1+cos 𝑥)+𝑠𝑒𝑛 𝑥 (1−cos 𝑥)
(1+cos 𝑥)2
G’(x) =
𝑠𝑒𝑛+𝑠𝑒𝑛 𝑥 cos 𝑥+𝑠𝑒𝑛 𝑥−𝑠𝑒𝑛 𝑥 𝑐𝑜𝑠𝑥
(1+cos 𝑥)2
G’(x) =
2 𝑠𝑒𝑛 𝑥
(1+cos 𝑥)2
d) Y = x2 . 2x
Y’= x2 . (2x)’ + (x2)’ (2x)
Y’ = x2 . [2x ln 2] . (1) + 2x . 2x
Y’ = 2x [x2 ln 2 + 2x]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Ejercicios de derivadas
- 1. PROGRAMA NACIONAL DE FORMACIÓN EN DISTRIBUCIÓN Y LOGÍSTICA EJERCICIOS DE DERIVADAS Integrante: Rivero María CI: 28.019.069 Profesor: Efren Escalona Sección: DL1301
- 2. EJERCICIOS DE DERIVADAS Hallar las derivadas de las funciones indicadas. a) G (x) = 2x2 – 5 G’ (x) = 2 . 2x G’ (x) = 4x b) Y = (x - 1) (x - 2) (x - 3) Y = (x2 - 2x – x + 2) (x – 3) Y = x3 – 3x2 – 2x2 + 6x – x2 + 3x + 2x – 6 Y = x3 – 6x2 + 11x – 6 Y’ = 3x2 - 6. 2x + 11 Y’ = 3x2 – 12x + 11 c) G (x) = 𝟏−𝐜𝐨𝐬 𝒙 𝟏+𝐜𝐨𝐬 𝒙 G’(x) = (1+cos 𝑥) (1−cos 𝑥)′−(1+cos 𝑥)′ (1−cos 𝑥) (1+𝑐𝑜𝑠 𝑥)2 = (1+cos 𝑥) (–( 𝑠𝑒𝑛 𝑥)) −(−𝑠𝑒𝑛 𝑥)(1−cos 𝑥) (1+𝑐𝑜𝑠 𝑥)2 = 𝑠𝑒𝑛 𝑥 (1+cos 𝑥)+𝑠𝑒𝑛 𝑥 (1−cos 𝑥) (1+cos 𝑥)2 G’(x) = 𝑠𝑒𝑛+𝑠𝑒𝑛 𝑥 cos 𝑥+𝑠𝑒𝑛 𝑥−𝑠𝑒𝑛 𝑥 𝑐𝑜𝑠𝑥 (1+cos 𝑥)2 G’(x) = 2 𝑠𝑒𝑛 𝑥 (1+cos 𝑥)2 d) Y = x2 . 2x Y’= x2 . (2x)’ + (x2)’ (2x) Y’ = x2 . [2x ln 2] . (1) + 2x . 2x Y’ = 2x [x2 ln 2 + 2x]
- 3. e) Y = (x2 – 3x + 5)3 𝑑𝑦 𝑑𝑥 = 3 (x2 – 3x + 5)2 𝑑 𝑑𝑥 (x2 – 3x + 5) = 3 (x2 – 3x + 5) (2x – 3)