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Lesson Worksheet: Differentiation of Exponential Functions Mathematics • Higher Education

In this worksheet, we will practice finding the derivatives of exponential functions.

Q1:

Differentiate the function ๐‘ฆ=3๐‘’โˆ’5โˆš๐‘ฅ๏—๏Žข.

  • A๐‘ฆโ€ฒ=3๐‘’โˆ’53๐‘ฅ๏—๏Šฑ๏Žฃ๏Žข
  • B๐‘ฆโ€ฒ=3๐‘’+53๐‘ฅ๏Žก๏Žข
  • C๐‘ฆโ€ฒ=3๐‘’+53๐‘ฅ๏—๏Žก๏Žข
  • D๐‘ฆโ€ฒ=3๐‘’+53๐‘ฅ๏—๏Šฑ๏Žฃ๏Žข
  • E๐‘ฆโ€ฒ=3๐‘’โˆ’53๐‘ฅ๏—๏Žก๏Žข

Q2:

Differentiate ๐‘“(๐‘ฅ)=๐‘’๐‘ฅ๏—sec.

  • A๐‘“โ€ฒ(๐‘ฅ)=๐‘’๐‘ฅ(1โˆ’๐‘ฅ)๏—sectan
  • B๐‘“โ€ฒ(๐‘ฅ)=๐‘’๐‘ฅ๐‘ฅ๏—sectan
  • C๐‘“โ€ฒ(๐‘ฅ)=๐‘’๐‘ฅ(1+๐‘ฅ)๏—sectan
  • D๐‘“โ€ฒ(๐‘ฅ)=๐‘ฅ(1+๐‘’๐‘ฅ)sectan๏—
  • E๐‘“โ€ฒ(๐‘ฅ)=๐‘’๏€น๐‘ฅ+๐‘ฅ๏…๏—๏Šจsectan

Q3:

If ๐‘“(๐‘ฅ)=โˆ’5๐‘’๏Šฑ๏Šฏ๏—, find ๐‘“(๐‘ฅ)๏Ž˜.

  • Aโˆ’18๐‘’๏Šฑ๏Šฏ๏—
  • Bโˆ’5๐‘’๏Šฑ๏Šง๏Šฆ๏—
  • C๐‘’๏Šฑ๏Šฏ๏—
  • Dโˆ’5๐‘’๏Šฑ๏Šฎ๏—
  • E45๐‘’๏Šฑ๏Šฏ๏—

Q4:

Determine the derivative of ๐‘”(๐‘ฅ)=โˆ’5๐‘’๏Šฑ๏Šฉ๏—๏Šฐ๏Šฉ๏—๏Žก.

  • A๐‘”โ€ฒ(๐‘ฅ)=๐‘’๏€น30๐‘ฅโˆ’15๏…๏Šฑ๏Šฉ๏—๏Šฐ๏Šฉ๏—๏Šจ๏Žก
  • B๐‘”โ€ฒ(๐‘ฅ)=5๐‘’๏Šฑ๏Šฉ๏—๏Šฐ๏Šฉ๏—๏Žก
  • C๐‘”โ€ฒ(๐‘ฅ)=๐‘’(30๐‘ฅโˆ’15)๏Šฑ๏Šฉ๏—๏Šฐ๏Šฉ๏—๏Žก
  • D๐‘”โ€ฒ(๐‘ฅ)=โˆ’5๐‘’๏Šฑ๏Šฉ๏—๏Šฐ๏Šฉ๏—๏Žก
  • E๐‘”โ€ฒ(๐‘ฅ)=๐‘’๏€น15๐‘ฅโˆ’15๐‘ฅ๏…๏Šฑ๏Šฉ๏—๏Šฐ๏Šฉ๏—๏Šจ๏Žก

Q5:

Find the first derivative of the function ๐‘ฆ=4๐‘’7๐‘ฅ+4๏Šญ๏—.

  • A196๐‘ฅ๐‘’+84๐‘’(7๐‘ฅ+4)๏Šญ๏—๏Šญ๏—๏Šจ
  • Bโˆ’196๐‘ฅ๐‘’+84๐‘’(7๐‘ฅ+4)๏Šญ๏—๏Šญ๏—๏Šจ
  • C196๐‘’+84๐‘’(7๐‘ฅ+4)๏Šญ๏—๏Šญ๏—๏Šจ
  • Dโˆ’28๐‘ฅ๐‘’+84๐‘’(7๐‘ฅ+4)๏Šญ๏—๏Šญ๏—๏Šจ
  • E196๐‘ฅ๐‘’+84๐‘’7๐‘ฅ+4๏Šญ๏—๏Šญ๏—

Q6:

If ๐‘ฆ=โˆ’3ร—2๏—, determine dd๐‘ฆ๐‘ฅ.

  • Aโˆ’62ln
  • Bโˆ’3ร—22๏—๏—ln
  • Cโˆ’3ร—22๏—ln
  • Dโˆ’62ln๏—

Q7:

Find the first derivative of the function ๐‘ฆ=๏€น7๏…๏Šฑ๏Šฏ๏—๏Šฑ๏Šฎ๏Šฑ๏Šจ.

  • A๏€น7๏…7๏Šง๏Šฎ๏—๏Šฐ๏Šง๏Šฌln
  • Bโˆ’2๏€น7๏…ln๏Šฑ๏Šฏ๏—๏Šฑ๏Šฎ
  • C18๏€น7๏…7๏Šง๏Šฎ๏—๏Šฐ๏Šง๏Šฌln
  • Dโˆ’2๏€น7๏…๏Šฑ๏Šฏ๏—๏Šฑ๏Šฎ๏Šฑ๏Šฉ

Q8:

A factoryโ€™s production of ๐‘ฆ units in day ๐‘ก is governed by the relation ๐‘ฆ=400๏€น10โˆ’๐‘’๏…๏Šฑ๏Šฆ๏Ž–๏Šฎ๏. What is the rate of change of production with respect to time on the fifth day?

  • A0.8๐‘’๏Šช
  • B320๐‘’๏Šช
  • Cโˆ’400๐‘’๏Šช
  • D320๐‘’๏Šช

Q9:

Find the derivative of the function ๐‘ฆ=โˆš3๐‘ฅ๐‘’+4๏Šฑ๏Šช๏—.

  • A๐‘ฆ=โˆ’3๐‘’๏€น4๐‘ฅ๐‘’โˆ’1๏…2โˆš3๐‘ฅ๐‘’+4๏Ž˜๏Šฑ๏Šช๏—๏Šช๏—๏Šฑ๏Šช๏—
  • B๐‘ฆ=6๐‘’(โˆ’4๐‘ฅ+1)โˆš3๐‘ฅ๐‘’+4๏Ž˜๏Šฑ๏Šช๏—๏Šฑ๏Šช๏—
  • C๐‘ฆ=3๐‘’(๐‘ฅ+1)2โˆš3๐‘ฅ๐‘’+4๏Ž˜๏Šฑ๏Šช๏—๏Šฑ๏Šช๏—
  • D๐‘ฆ=โˆ’6๐‘’(โˆ’4๐‘ฅ+1)โˆš3๐‘ฅ๐‘’+4๏Ž˜๏Šฑ๏Šช๏—๏Šฑ๏Šช๏—
  • E๐‘ฆ=3๐‘’(โˆ’4๐‘ฅ+1)2โˆš3๐‘ฅ๐‘’+4๏Ž˜๏Šฑ๏Šช๏—๏Šฑ๏Šช๏—

Q10:

Find the derivative of the function ๐‘“(๐‘ง)=โˆ’3๐‘’๏Žฃ๏‘’๏Žฃ๏‘’๏Žฉ๏Ž .

  • A๐‘“โ€ฒ(๐‘ง)=3๐‘’(4๐‘ง+1)๏Žฃ๏‘’๏Žฃ๏‘’๏Žฉ๏Ž ๏Šจ
  • B๐‘“โ€ฒ(๐‘ง)=12๐‘’(4๐‘ง+1)๏Žฃ๏‘’๏Žฃ๏‘’๏Žฉ๏Ž ๏Šจ
  • C๐‘“โ€ฒ(๐‘ง)=โˆ’12๐‘’4๐‘ง+1๏Žฃ๏‘’๏Žฃ๏‘’๏Žฉ๏Ž 
  • D๐‘“โ€ฒ(๐‘ง)=โˆ’3๐‘’(4๐‘ง+1)๏Žฃ๏‘’๏Žฃ๏‘’๏Žฉ๏Ž ๏Šจ
  • E๐‘“โ€ฒ(๐‘ง)=โˆ’12๐‘’(4๐‘ง+1)๏Žฃ๏‘’๏Žฃ๏‘’๏Žฉ๏Ž ๏Šจ

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