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Lesson: Using the Chain Rule for the Derivatives of Single-Variable Functions

In this lesson, we will learn how to use chain rule of derivatives of single-variable functions.

Sample Question Videos

03:22

Worksheet • 25 Questions • 1 Video

Q1:

Find the first derivative of the function 𝑦 = ο€Ή 5 π‘₯ βˆ’ 6  2 6 .

  • A 6 0 π‘₯ ο€Ή 5 π‘₯ βˆ’ 6  2 5
  • B 6 ο€Ή 5 π‘₯ βˆ’ 6  2 5
  • C 6 ο€Ή 5 π‘₯ βˆ’ 6  2 7
  • D 6 0 π‘₯ ο€Ή 5 π‘₯ βˆ’ 6  2 7

Q2:

Find the first derivative of the function 𝑦 = 𝑒 7 π‘₯ π‘₯ s i n .

  • A 𝑒 7 π‘₯ + 7 𝑒 7 π‘₯ π‘₯ π‘₯ s i n c o s
  • B βˆ’ 𝑒 7 π‘₯ + 7 𝑒 7 π‘₯ π‘₯ π‘₯ s i n c o s
  • C 𝑒 7 π‘₯ βˆ’ 7 𝑒 7 π‘₯ π‘₯ π‘₯ s i n c o s
  • D βˆ’ 𝑒 7 π‘₯ βˆ’ 7 𝑒 7 π‘₯ π‘₯ π‘₯ s i n c o s

Q3:

Determine the derivative of the function 𝑓 ( 𝑑 ) = 4 𝑒 5 𝑑 𝑑 s i n .

  • A 𝑓 β€² ( 𝑑 ) = 2 0 𝑒 ( 𝑑 𝑑 + 𝑑 ) 5 𝑑 𝑑 s i n c o s s i n
  • B 𝑓 β€² ( 𝑑 ) = βˆ’ 2 0 𝑒 ( 𝑑 𝑑 βˆ’ 𝑑 ) 5 𝑑 𝑑 s i n c o s s i n
  • C 𝑓 β€² ( 𝑑 ) = βˆ’ 4 𝑒 ( 𝑑 βˆ’ 5 ) 5 𝑑 𝑑 s i n c o s
  • D 𝑓 β€² ( 𝑑 ) = 4 𝑒 ( 𝑑 + 5 ) 5 𝑑 𝑑 s i n c o s
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