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Lesson: Differentiation of Natural Exponential Functions

In this lesson, we will learn how to differentiate natural exponential functions without taking limits of the function.

Sample Question Videos

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Worksheet • 20 Questions • 3 Videos

Q1:

Find the first derivative of the function 𝑦 = 3 𝑒 4 7 π‘₯ s e c .

  • A 8 4 𝑒 7 π‘₯ 7 π‘₯ 4 7 π‘₯ s e c s e c t a n
  • B 1 2 𝑒 7 π‘₯ 7 π‘₯ 4 7 π‘₯ s e c s e c t a n
  • C 3 𝑒 4 7 π‘₯ s e c
  • D βˆ’ 8 4 𝑒 7 π‘₯ 7 π‘₯ 4 7 π‘₯ s e c s e c t a n
  • E 8 4 𝑒 7 π‘₯ 4 7 π‘₯ 2 s e c t a n

Q2:

Find the first derivative of the function 𝑦 = 𝑒 3 βˆ’ 4 π‘₯ βˆ’ 3 3 .

  • A βˆ’ 4 π‘₯ 𝑒 2 ( βˆ’ 4 π‘₯ βˆ’ 3 ) 1 3 3
  • B 𝑒 1 3 3 ( βˆ’ 4 π‘₯ βˆ’ 3 )
  • C βˆ’ 3 6 π‘₯ 𝑒 2 ( βˆ’ 4 π‘₯ βˆ’ 3 ) 1 3 3
  • D βˆ’ 4 π‘₯ 𝑒 3 ( βˆ’ 4 π‘₯ βˆ’ 3 ) 1 3 3

Q3:

Differentiate 𝑧 ( 𝑦 ) = 𝐴 5 𝑦 + 𝐡 𝑒 3 3 𝑦 .

  • A d d 𝑧 𝑦 = βˆ’ 3 𝐴 5 𝑦 + 3 𝐡 𝑒 4 3 𝑦
  • B d d 𝑧 𝑦 = 𝐴 5 𝑦 + 𝐡 𝑒 2 3 𝑦
  • C d d 𝑧 𝑦 = βˆ’ 3 𝐴 5 𝑦 + 3 𝐡 𝑒 2 3 𝑦
  • D d d 𝑧 𝑦 = βˆ’ 3 𝐴 5 𝑦 + 3 𝐡 𝑒 3 3 𝑦
  • E d d 𝑧 𝑦 = 𝐴 5 𝑦 + 𝐡 𝑒 4 3 𝑦
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