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TALLER DE CALCULO II DE 28/03/2019 NOMBRE: Pimentel Gonzales, Jhessica Ethel

CUI: 20182881

Ejercicio 1: Halle la derivada de la siguiente funciรณn.

๐‘ฆ = log [

โˆš1+๐‘ฅ+โˆš1โˆ’๐‘ฅ ] โˆš1+๐‘ฅโˆ’โˆš1โˆ’๐‘ฅ

๐‘ฆ = ln ( โˆš1 + ๐‘ฅ + โˆš1 โˆ’ ๐‘ฅ ) โˆ’ ln(โˆš1 + ๐‘ฅ โˆ’ โˆš1 โˆ’ ๐‘ฅ)

๐‘ฆยด = ๐‘ฆยด =

1

1

(

โˆš1+๐‘ฅ+โˆš1โˆ’๐‘ฅ 2โˆš1+๐‘ฅ 1

2(โˆš1 + ๐‘ฅ + โˆš1 โˆ’ ๐‘ฅ)

(

โˆ’

1 2โˆš1โˆ’๐‘ฅ

โˆš1 โˆ’ ๐‘ฅ โˆ’ โˆš1 + ๐‘ฅ โˆš1 โˆ’

๐‘ฅ2

)โˆ’

)โˆ’

1

(

1

โˆš1+๐‘ฅโˆ’โˆš1โˆ’๐‘ฅ 2โˆš1+๐‘ฅ 1

2(โˆš1 + ๐‘ฅ โˆ’ โˆš1 โˆ’ ๐‘ฅ )

(

+

1 2โˆš1โˆ’๐‘ฅ

)

โˆš1 โˆ’ ๐‘ฅ + โˆš1 + ๐‘ฅ โˆš1 โˆ’ ๐‘ฅ 2

)

๐‘ฆยด =

โˆ’(โˆš1 โˆ’ ๐‘ฅ โˆ’ โˆš1 + ๐‘ฅ)(โˆ’โˆš1 + ๐‘ฅ + โˆš1 โˆ’ ๐‘ฅ) โˆ’ (โˆš1 โˆ’ ๐‘ฅ + โˆš1 + ๐‘ฅ)(โˆš1 + ๐‘ฅ + โˆš1 โˆ’ ๐‘ฅ) 2โˆš1 โˆ’ ๐‘ฅ 2 (โˆš1 + ๐‘ฅ + โˆš1 โˆ’ ๐‘ฅ)(โˆš1 + ๐‘ฅ โˆ’ โˆš1 โˆ’ ๐‘ฅ) 2

๐‘ฆยด = ๐‘ฆยด =

โˆ’(โˆš(1โˆ’๐‘ฅ)โˆ’โˆš(1+๐‘ฅ)) โˆ’(โˆš(1+๐‘ฅ)+โˆš(1โˆ’๐‘ฅ))2 2โˆš1โˆ’๐‘ฅ 2 (2๐‘ฅ) โˆ’4 4๐‘ฅโˆš1โˆ’๐‘ฅ 2

๐‘ฆยด = โˆ’

1 ๐‘ฅโˆš1โˆ’๐‘ฅ 2

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