CALCULO DIFERENCIAL

𝑓 + 𝑔 𝑥 = 𝑓 𝑥 + 𝑔 𝑥

𝑓 𝑥 = 2𝑥 + 1 𝑔 𝑥 = 𝑥2

𝑓 + 𝑔 𝑥 = 2𝑥 + 1 + 𝑥2

= 𝑥2 + 2𝑥 + 1

𝑓 + 𝑔 3 = 2𝑥 + 1 + 𝑥2

= (3)2+2 3 + 1= 9 + 6 + 1= 16

SUMA

𝑓 − 𝑔 𝑥 = 𝑓 𝑥 − 𝑔 𝑥

𝑓 𝑥 = 2𝑥 + 1 𝑔 𝑥 = 𝑥2

𝑓 − 𝑔 𝑥 = 2𝑥 + 1 − 𝑥2

= −𝑥2 + 2𝑥 + 1

𝑓 − 𝑔 3 = 2𝑥 + 1 − 𝑥2

= −(3)2 + 2 3 + 1= −9 + 6 + 1

= −2

RESTA

𝑓 ∗ 𝑔 𝑥 = 𝑓 𝑥 ∗ 𝑔 𝑥

𝑓 𝑥 = 2𝑥 + 1 𝑔 𝑥 = 𝑥2

𝑓 ∗ 𝑔 𝑥 = 2𝑥 + 1 ∗ 𝑥2

= 2𝑥3 + 𝑥2

𝑓 ∗ 𝑔 3 = 2𝑥 + 1 ∗ 𝑥2

= [2(3) + 1] ∗ 32

= 6 + 1 ∗ 9= 7 ∗ 9= 42

MULTIPLICACION O PRODUCTO

𝑓

𝑔𝑥 =

𝑓(𝑥)𝑔(𝑥)

𝑓 𝑥 = 2𝑥 + 1 𝑔 𝑥 = 𝑥2

𝑓

𝑔𝑥 = 2𝑥 + 1

𝑥2

=2

𝑥+1

𝑥2

𝑓

𝑔3 = 2𝑥 + 1

𝑥2

= 2(3) + 1

32

= 6 + 19

= 7 9

DIVISION O COCIENTE

𝑓 𝑜 𝑔 𝑥 = 𝑓 𝑔(𝑥)

𝑓 𝑥 = 2𝑥 + 1 𝑔 𝑥 = 𝑥2

𝑓 𝑜 𝑔 𝑥 = 2 𝑥2 + 1= 2𝑥2 + 1

𝑓 𝑜 𝑔 3 = 2 𝑥2 + 1= 2 32 + 1= 2 9 + 1= 18 + 1= 19

FUNCION COMPUESTA

𝑔 𝑜 𝑓 𝑥 = 𝑔 𝑓(𝑥)

𝑓 𝑥 = 2𝑥 + 1 𝑔 𝑥 = 𝑥2

𝑔 𝑜 𝑓 𝑥 = (2𝑥 + 1)2

= (2𝑥 + 1)2= 4𝑥2 + 4𝑥 + 1

𝑔 𝑜 𝑓 3 = (2(3) + 1)2

= (6 + 1)2

= (7)2

= 49

W. SWOKOWSKI, Earl, Cálculo con Geometría

Analítica, 2da. Edición, Panamericana, Colombia, 1989, 1097 págs.

BIBLIOGRAFIA