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Lesson: Logarithmic Differentiation

Sample Question Videos

Worksheet • 18 Questions • 1 Video

Q1:

Use logarithmic differentiation to find the derivative of the function 𝑦 = 2 ( π‘₯ ) c o s π‘₯ .

  • A 𝑦 β€² = 2 ( π‘₯ ) [ π‘₯ βˆ’ π‘₯ π‘₯ ] c o s l n c o s t a n π‘₯
  • B 𝑦 β€² = π‘₯ βˆ’ π‘₯ π‘₯ l n c o s t a n
  • C 𝑦 β€² = 2 ( π‘₯ ) [ π‘₯ + π‘₯ π‘₯ ] c o s l n c o s t a n π‘₯
  • D 𝑦 β€² = [ π‘₯ + π‘₯ π‘₯ ] [ π‘₯ βˆ’ π‘₯ π‘₯ ] l n c o s c o t l n c o s t a n
  • E 𝑦 β€² = 2 ( π‘₯ ) [ π‘₯ βˆ’ π‘₯ π‘₯ ] c o s l n c o s c o t π‘₯

Q2:

Given that 𝑦 = ( 8 π‘₯ ) l o g 4 5 π‘₯ t a n , find d d 𝑦 π‘₯ .

  • A ( 8 π‘₯ )  2 0 ( 8 π‘₯ ) 5 π‘₯ + 4 5 π‘₯ π‘₯ 1 0 8 π‘₯  l o g l n l o g s e c t a n l n l o g 4 5 π‘₯ 2 t a n
  • B 2 0 ( 8 π‘₯ ) 5 π‘₯ + 4 5 π‘₯ π‘₯ 1 0 8 π‘₯ l n l o g s e c t a n l n l o g 2
  • C ( 8 π‘₯ )  2 0 ( 8 π‘₯ ) 5 π‘₯ + 4 5 π‘₯ π‘₯ 1 0  l o g l n l o g s e c t a n l n 4 5 π‘₯ 2 t a n
  • D 2 0 ( 8 π‘₯ ) 5 π‘₯ + 4 5 π‘₯ π‘₯ 8 π‘₯ l n l o g s e c t a n l o g 2

Q3:

Determine d d 𝑦 π‘₯ , given that 𝑦 = ( 8 4 π‘₯ ) s i n 2 π‘₯ .

  • A 2 ( 8 4 π‘₯ ) [ ( 8 4 π‘₯ ) + 4 π‘₯ 4 π‘₯ ] s i n l n s i n c o t 2 π‘₯
  • B ( 8 4 π‘₯ ) [ ( 4 π‘₯ ) + π‘₯ 4 π‘₯ ] s i n l n s i n t a n 2 π‘₯
  • C 1 6 π‘₯ ( 4 π‘₯ ) l n c o s
  • D 1 6 π‘₯ 4 π‘₯ c o s
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