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Hoja de actividades: Derivar funciones logarítmicas arbitrarias

P1:

Halla la primera derivada de la funciรณn ๐‘ฆ = โˆ’ 8 ๐‘’ + 2 ๏€ผ 7 ๐‘ฅ 2 ๏ˆ ๏Šญ ๏— ๏Šซ l o g .

  • A โˆ’ 5 6 ๐‘’ + 1 ๐‘ฅ 5 ๏Šญ ๏— l n
  • B โˆ’ 5 6 ๐‘’ + 2 ๐‘ฅ ๏Šญ ๏—
  • C โˆ’ 8 ๐‘’ + 2 ๐‘ฅ 5 ๏Šญ ๏— l n
  • D โˆ’ 5 6 ๐‘’ + 2 ๐‘ฅ 5 ๏Šญ ๏— l n

P2:

Halla d d ๐‘ฆ ๐‘ฅ , dado que ๐‘ฆ = 7 ( 7 ๐‘ฅ + 3 ) l o g ๏Šช .

  • A 4 9 ๐‘ฅ + 2 1 7 4 l n
  • B 7 ( 7 ๐‘ฅ + 3 ) 4 l o g
  • C 4 9 ๐‘ฅ + 2 1 7 4 l o g
  • D 4 9 ( 7 ๐‘ฅ + 3 ) 4 l n

P3:

Halla la primera derivada de ๐‘ฆ = ( 4 ๐‘ฅ ) + โˆš 3 ๐‘ฅ ๐‘ฅ l o g l o g ๏Šฏ ๏Šฏ .

  • A 9 ( 4 ๐‘ฅ ) ( 1 0 ) ๐‘ฅ + โˆš 3 ๐‘ฅ ๐‘ฅ ๐‘ฅ + 9 โˆš 3 ๐‘ฅ ( 1 0 ) ๐‘ฅ l o g l n l o g l n ๏Šฎ ๏Šฏ
  • B 9 ( 4 ๐‘ฅ ) ๐‘ฅ + โˆš 3 ๐‘ฅ ๐‘ฅ 2 ๐‘ฅ + 9 โˆš 3 ๐‘ฅ ๐‘ฅ l o g l o g ๏Šฎ ๏Šฏ
  • C 9 ( 4 ๐‘ฅ ) 1 0 + โˆš 3 ๐‘ฅ ๐‘ฅ 2 ๐‘ฅ + 9 โˆš 3 ๐‘ฅ 1 0 l o g l n l o g l n ๏Šฎ ๏Šฏ
  • D 9 ( 4 ๐‘ฅ ) ( 1 0 ) ๐‘ฅ + โˆš 3 ๐‘ฅ ๐‘ฅ 2 ๐‘ฅ + 9 โˆš 3 ๐‘ฅ ( 1 0 ) ๐‘ฅ l o g l n l o g l n ๏Šฎ ๏Šฏ

P4:

Halla la primera derivada de ๐‘ฆ = ( 5 ๐‘ฅ ) + โˆš 2 ๐‘ฅ 9 ๐‘ฅ l o g l o g ๏Šฉ ๏Šช .

  • A 3 ( 5 ๐‘ฅ ) ( 1 0 ) ๐‘ฅ + โˆš 2 ๐‘ฅ 9 ๐‘ฅ ๐‘ฅ + 4 โˆš 2 ๐‘ฅ ( 1 0 ) ๐‘ฅ l o g l n l o g l n ๏Šจ ๏Šช
  • B 3 ( 5 ๐‘ฅ ) ๐‘ฅ + โˆš 2 ๐‘ฅ 9 ๐‘ฅ 2 ๐‘ฅ + 4 โˆš 2 ๐‘ฅ ๐‘ฅ l o g l o g ๏Šจ ๏Šช
  • C 3 ( 5 ๐‘ฅ ) 1 0 + โˆš 2 ๐‘ฅ 9 ๐‘ฅ 2 ๐‘ฅ + 4 โˆš 2 ๐‘ฅ 1 0 l o g l n l o g l n ๏Šจ ๏Šช
  • D 3 ( 5 ๐‘ฅ ) ( 1 0 ) ๐‘ฅ + โˆš 2 ๐‘ฅ 9 ๐‘ฅ 2 ๐‘ฅ + 4 โˆš 2 ๐‘ฅ ( 1 0 ) ๐‘ฅ l o g l n l o g l n ๏Šจ ๏Šช

P5:

Dado ๐‘ฆ = ๏„ž โˆ’ 7 ๐‘ฅ + 5 8 ๐‘ฅ โˆ’ 9 l o g , halla d d ๐‘ฆ ๐‘ฅ .

  • A 2 3 ( โˆ’ 7 ๐‘ฅ + 5 ) ( 8 ๐‘ฅ โˆ’ 9 ) 1 0 l n
  • B 2 3 2 ( โˆ’ 7 ๐‘ฅ + 5 ) ( 8 ๐‘ฅ โˆ’ 9 )
  • C โˆ’ 2 3 2 ( โˆ’ 7 ๐‘ฅ + 5 ) ( 8 ๐‘ฅ โˆ’ 9 ) 1 0 l n
  • D 2 3 2 ( โˆ’ 7 ๐‘ฅ + 5 ) ( 8 ๐‘ฅ โˆ’ 9 ) 1 0 l n

P6:

Dado ๐‘ฆ = ๏„ž โˆ’ ๐‘ฅ + 9 5 ๐‘ฅ โˆ’ 3 l o g , halla d d ๐‘ฆ ๐‘ฅ .

  • A โˆ’ 4 2 ( โˆ’ ๐‘ฅ + 9 ) ( 5 ๐‘ฅ โˆ’ 3 ) 1 0 l n
  • B โˆ’ 2 1 ( โˆ’ ๐‘ฅ + 9 ) ( 5 ๐‘ฅ โˆ’ 3 )
  • C 2 1 ( โˆ’ ๐‘ฅ + 9 ) ( 5 ๐‘ฅ โˆ’ 3 ) 1 0 l n
  • D โˆ’ 2 1 ( โˆ’ ๐‘ฅ + 9 ) ( 5 ๐‘ฅ โˆ’ 3 ) 1 0 l n

P7:

Siendo ๐‘ฆ = 5 3 ๐‘ฅ 5 3 ๐‘ฅ โˆ’ 6 l o g l o g , halla d d ๐‘ฆ ๐‘ฅ .

  • A โˆ’ 6 ๐‘ฅ ( 5 3 ๐‘ฅ โˆ’ 6 ) l o g ๏Šจ
  • B โˆ’ 3 0 ๐‘’ ๐‘ฅ ( 5 3 ๐‘ฅ โˆ’ 6 ) l o g l o g
  • C 5 ( 1 0 3 ๐‘ฅ โˆ’ 6 ) ๐‘’ ๐‘ฅ ( 5 3 ๐‘ฅ โˆ’ 6 ) l o g l o g l o g ๏Šจ
  • D โˆ’ 3 0 ๐‘’ ๐‘ฅ ( 5 3 ๐‘ฅ โˆ’ 6 ) l o g l o g ๏Šจ

P8:

Halla d d ๐‘ฆ ๐‘ฅ , dado que ๐‘ฆ = ( 7 ๐‘ฅ โˆ’ 1 ) l o g ๏Šฏ .

  • A 7 ๐‘ฅ โˆ’ 1 6 3 1 0 l n
  • B 7 ( 7 ๐‘ฅ โˆ’ 1 ) 1 0 ๏Šฏ l o g
  • C ( 7 ๐‘ฅ โˆ’ 1 ) 7 1 0 ๏Šฏ l o g
  • D 6 3 ( 7 ๐‘ฅ โˆ’ 1 ) 1 0 l n

P9:

Halla d d ๐‘ฆ ๐‘ฅ , dado que ๐‘ฆ = โˆ’ 7 ( 5 ๐‘ฅ + 3 ) l o g ๏Šฌ .

  • A โˆ’ 3 5 ๐‘ฅ โˆ’ 2 1 3 0 1 0 l n
  • B โˆ’ 3 5 ( 5 ๐‘ฅ + 3 ) 1 0 ๏Šฌ l o g
  • C โˆ’ 7 ( 5 ๐‘ฅ + 3 ) 5 1 0 ๏Šฌ l o g
  • D โˆ’ 2 1 0 ( 5 ๐‘ฅ + 3 ) 1 0 l n

P10:

Halla d d ๐‘ฆ ๐‘ฅ , dado que ๐‘ฆ = 3 ( 4 ๐‘ฅ โˆ’ 7 ) l o g ๏Šช .

  • A 1 2 ๐‘ฅ โˆ’ 2 1 1 6 1 0 l n
  • B 1 2 ( 4 ๐‘ฅ โˆ’ 7 ) 1 0 ๏Šช l o g
  • C 3 ( 4 ๐‘ฅ โˆ’ 7 ) 4 1 0 ๏Šช l o g
  • D 4 8 ( 4 ๐‘ฅ โˆ’ 7 ) 1 0 l n

P11:

Halla d d ๐‘ฆ ๐‘ฅ , siendo ๐‘ฆ = ๏€น 2 5 ๐‘ฅ ๏… l o g c o s ๏Šญ .

  • A โˆ’ 3 5 ๐‘ฅ 5 ๐‘ฅ 5 ๐‘ฅ ๏Šฌ ๏Šญ ๏Šญ s e n c o s
  • B 3 5 ๐‘ฅ 5 ๐‘ฅ ( 1 0 ) 5 ๐‘ฅ ๏Šฌ ๏Šญ ๏Šญ s e n l n c o s
  • C โˆ’ 7 0 ๐‘ฅ 5 ๐‘ฅ ๏Šฌ ๏Šญ s e n
  • D โˆ’ 3 5 ๐‘ฅ 5 ๐‘ฅ ( 1 0 ) 5 ๐‘ฅ ๏Šฌ ๏Šญ ๏Šญ s e n l n c o s

P12:

Halla d d ๐‘ฆ ๐‘ฅ , siendo ๐‘ฆ = ๏€น 6 5 ๐‘ฅ ๏… l o g s e n ๏Šช .

  • A 2 0 ๐‘ฅ 5 ๐‘ฅ 5 ๐‘ฅ ๏Šฉ ๏Šช ๏Šช c o s s e n
  • B โˆ’ 2 0 ๐‘ฅ 5 ๐‘ฅ ( 1 0 ) 5 ๐‘ฅ ๏Šฉ ๏Šช ๏Šช c o s l n s e n
  • C 1 2 0 ๐‘ฅ 5 ๐‘ฅ ๏Šฉ ๏Šช c o s
  • D 2 0 ๐‘ฅ 5 ๐‘ฅ ( 1 0 ) 5 ๐‘ฅ ๏Šฉ ๏Šช ๏Šช c o s l n s e n

P13:

Deriva ๐‘“ ( ๐‘ฅ ) = ( 4 3 ๐‘ฅ + 3 ) l o g c o s ๏Šง ๏Šฆ .

  • A ๐‘“ โ€ฒ ( ๐‘ฅ ) = โˆ’ 4 3 ๐‘ฅ โˆ’ 3 1 2 1 0 3 ๐‘ฅ c o s l n s e n
  • B ๐‘“ โ€ฒ ( ๐‘ฅ ) = 1 2 3 ๐‘ฅ ( 4 3 ๐‘ฅ + 3 ) 1 0 s e n c o s l n
  • C ๐‘“ โ€ฒ ( ๐‘ฅ ) = โˆ’ 1 2 3 ๐‘ฅ 4 3 ๐‘ฅ + 3 s e n c o s
  • D ๐‘“ โ€ฒ ( ๐‘ฅ ) = โˆ’ 1 2 3 ๐‘ฅ ( 4 3 ๐‘ฅ + 3 ) 1 0 s e n c o s l n

P14:

Deriva ๐‘“ ( ๐‘ฅ ) = ( โˆ’ 4 ๐‘ฅ + 3 ) l o g c o s ๏Šง ๏Šฆ .

  • A ๐‘“ โ€ฒ ( ๐‘ฅ ) = โˆ’ 4 ๐‘ฅ โˆ’ 3 4 1 0 4 ๐‘ฅ c o s l n s e n
  • B ๐‘“ โ€ฒ ( ๐‘ฅ ) = โˆ’ 4 4 ๐‘ฅ ( โˆ’ 4 ๐‘ฅ + 3 ) 1 0 s e n c o s l n
  • C ๐‘“ โ€ฒ ( ๐‘ฅ ) = 4 4 ๐‘ฅ โˆ’ 4 ๐‘ฅ + 3 s e n c o s
  • D ๐‘“ โ€ฒ ( ๐‘ฅ ) = 4 4 ๐‘ฅ ( โˆ’ 4 ๐‘ฅ + 3 ) 1 0 s e n c o s l n

P15:

Dado que ๐‘ฆ = โˆ’ 2 ( 9 ๐‘ฅ ) c o s l o g ๏Šจ , halla d d ๐‘ฆ ๐‘ฅ .

  • A 4 ( 9 ๐‘ฅ ) ๐‘ฅ 1 0 s e n l o g l n ๏Šจ
  • B โˆ’ 4 9 ๐‘ฅ ( 9 ๐‘ฅ ) ๐‘ฅ 1 0 l o g s e n l o g l n ๏Šจ
  • C โˆ’ 4 ( 9 ๐‘ฅ ) ๐‘ฅ 1 0 s e n l o g l n ๏Šจ
  • D 4 9 ๐‘ฅ ( 9 ๐‘ฅ ) ๐‘ฅ 1 0 l o g s e n l o g l n ๏Šจ

P16:

Halla d d ๐‘ฆ ๐‘ฅ siendo ๐‘ฆ = โˆš 6 ๐‘ฅ l o g ๏Žข ๏Šช .

  • A 4 ๐‘ฅ 3 1 0 l n
  • B 4 3 ๐‘ฅ
  • C 3 4 ( 1 0 ) ๐‘ฅ l n
  • D 4 3 ( 1 0 ) ๐‘ฅ l n

P17:

Halla d d ๐‘ฆ ๐‘ฅ siendo ๐‘ฆ = โˆš 3 ๐‘ฅ l o g ๏Žค ๏Šญ .

  • A 7 ๐‘ฅ 5 1 0 l n
  • B 7 5 ๐‘ฅ
  • C 5 7 ( 1 0 ) ๐‘ฅ l n
  • D 7 5 ( 1 0 ) ๐‘ฅ l n