Worksheet: Differentiation of Exponential Functions

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

Q1:

Find the first derivative of the function 𝑦=4𝑥+2𝑒.

  • A24𝑥2𝑒
  • B4𝑥+2𝑒
  • C24𝑥+2𝑒
  • D24𝑥+2

Q2:

Differentiate the function 𝑦=3𝑒5𝑥.

  • A𝑦=3𝑒53𝑥
  • B𝑦=3𝑒+53𝑥
  • C𝑦=3𝑒+53𝑥
  • D𝑦=3𝑒+53𝑥
  • E𝑦=3𝑒53𝑥

Q3:

Find the first derivative of the function 𝑦=2𝑒5𝑒.

  • A42𝑒5𝑒
  • B2𝑒5𝑒8𝑒+25𝑒
  • C42𝑒5𝑒8𝑒+25𝑒
  • D42𝑒5𝑒8𝑒+25𝑒
  • E42𝑒5𝑒8𝑒+25𝑒

Q4:

Differentiate (𝑡)=5𝑡𝑒.

  • A(𝑡)=53𝑡𝑒
  • B(𝑡)=5𝑡𝑒
  • C(𝑡)=53𝑡𝑒
  • D(𝑡)=53𝑡𝑒
  • E(𝑡)=53𝑡𝑒

Q5:

Find dd𝑦𝑥 if 5𝑦𝑒=7𝑒.

  • A𝑦
  • B25𝑦
  • C75𝑦
  • D2𝑦
  • E2𝑦

Q6:

Determine the derivative of 𝑔(𝑥)=5𝑒.

  • A𝑔(𝑥)=𝑒30𝑥15
  • B𝑔(𝑥)=5𝑒
  • C𝑔(𝑥)=𝑒(30𝑥15)
  • D𝑔(𝑥)=5𝑒
  • E𝑔(𝑥)=𝑒15𝑥15𝑥

Q7:

Find the derivative of the function 𝑦=5𝑥𝑒.

  • A𝑦=52𝑥𝑒+1
  • B𝑦=5𝑒(2𝑥1)
  • C𝑦=52𝑥𝑒1
  • D𝑦=10𝑥𝑒𝑥
  • E𝑦=5𝑒(2𝑥1)

Q8:

Differentiate 𝑓(𝑥)=𝑒𝑥sec.

  • A𝑓(𝑥)=𝑒𝑥(1𝑥)sectan
  • B𝑓(𝑥)=𝑒𝑥𝑥sectan
  • C𝑓(𝑥)=𝑒𝑥(1+𝑥)sectan
  • D𝑓(𝑥)=𝑥(1+𝑒𝑥)sectan
  • E𝑓(𝑥)=𝑒𝑥+𝑥sectan

Q9:

Find the first derivative of the function 𝑦=4𝑒7𝑥+4.

  • A196𝑥𝑒+84𝑒(7𝑥+4)
  • B196𝑥𝑒+84𝑒(7𝑥+4)
  • C196𝑒+84𝑒(7𝑥+4)
  • D28𝑥𝑒+84𝑒(7𝑥+4)
  • E196𝑥𝑒+84𝑒7𝑥+4

Q10:

Find the first derivative of the function 𝑦=𝑒78𝑥tan.

  • A𝑒8𝑥88𝑥78𝑥tansectan
  • B𝑒58𝑥+88𝑥78𝑥tansectan
  • C𝑒(58𝑥88𝑥)78𝑥tansectan
  • D𝑒58𝑥88𝑥78𝑥tansectan
  • E𝑒58𝑥88𝑥78𝑥tansectan

Q11:

Find the derivative of the function 𝑓(𝑧)=3𝑒.

  • A𝑓(𝑧)=3𝑒(4𝑧+1)
  • B𝑓(𝑧)=12𝑒(4𝑧+1)
  • C𝑓(𝑧)=12𝑒4𝑧+1
  • D𝑓(𝑧)=3𝑒(4𝑧+1)
  • E𝑓(𝑧)=12𝑒(4𝑧+1)

Q12:

Find the derivative of the function 𝑦=5𝑒tan.

  • A𝑦=10𝑒𝜃tancsc
  • B𝑦=10𝑒𝜃tansec
  • C𝑦=10𝑒𝜃tancsc
  • D𝑦=10𝑒𝜃tantan
  • E𝑦=10𝑒𝜃tansec

Q13:

Find the first derivative of the function 𝑦=3𝑒sec.

  • A84𝑒7𝑥7𝑥secsectan
  • B12𝑒7𝑥7𝑥secsectan
  • C84𝑒7𝑥7𝑥secsectan
  • D84𝑒7𝑥sectan
  • E3𝑒sec

Q14:

Find the derivative of the function 𝑦=3𝑥𝑒+4.

  • A𝑦=3𝑒4𝑥𝑒123𝑥𝑒+4
  • B𝑦=6𝑒(4𝑥+1)3𝑥𝑒+4
  • C𝑦=3𝑒(𝑥+1)23𝑥𝑒+4
  • D𝑦=6𝑒(4𝑥+1)3𝑥𝑒+4
  • E𝑦=3𝑒(4𝑥+1)23𝑥𝑒+4

Q15:

Find the derivative of the function 𝑦=4𝑒+5𝑒+5cos.

  • A𝑦=4𝑒+5𝑒+5sin
  • B𝑦=40𝑒(𝑒+5)𝑒+5𝑒+5sin
  • C𝑦=40𝑒𝑒+5𝑒+5𝑒+5sin
  • D𝑦=4𝑒+5𝑒+5sin
  • E𝑦=40𝑒(𝑒+5)𝑒+5𝑒+5sin

Q16:

Find the derivative of the function 𝑓(𝑡)=𝑒sinsin.

  • A𝑓(𝑡)=2𝑒𝑒𝑒sinsinsinsincos
  • B𝑓(𝑡)=10𝑒𝑒5𝑡𝑒5𝑡sinsinsinsinsincoscos
  • C𝑓(𝑡)=20𝑒𝑒5𝑡𝑒5𝑡sinsinsinsinsincoscos
  • D𝑓(𝑡)=10𝑒𝑒5𝑡𝑒5𝑡sinsinsinsinsincoscos
  • E𝑓(𝑡)=20𝑒𝑒5𝑡𝑒5𝑡sinsinsinsinsincoscos

Q17:

Find 𝑓(4), if 𝑓(𝑥)=8𝑒.

  • A6𝑓(4)
  • B48𝑓(4)
  • C8𝑓(4)
  • D14𝑓(4)

Q18:

If 𝑓(𝑥)=5𝑒, find 𝑓(𝑥).

  • A18𝑒
  • B5𝑒
  • C𝑒
  • D5𝑒
  • E45𝑒

Q19:

Differentiate 𝑧(𝑦)=𝐴5𝑦+𝐵𝑒.

  • Add𝑧𝑦=3𝐴5𝑦+3𝐵𝑒
  • Bdd𝑧𝑦=𝐴5𝑦+𝐵𝑒
  • Cdd𝑧𝑦=3𝐴5𝑦+3𝐵𝑒
  • Ddd𝑧𝑦=𝐴5𝑦+𝐵𝑒
  • Edd𝑧𝑦=3𝐴5𝑦+3𝐵𝑒

Q20:

Find the first derivative of the function 𝑦=𝑒.

  • A4𝑥𝑒
  • B𝑒
  • C36𝑥𝑒
  • D4𝑥𝑒

Q21:

If 𝑦=3×2, determine dd𝑦𝑥.

  • A62ln
  • B3×22ln
  • C3×22ln
  • D62ln

Q22:

Find the derivative of the function 𝑦=2.

  • A𝑦=2572lnlnln
  • B𝑦=22ln
  • C𝑦=257257lnlnln
  • D𝑦=7257ln
  • E𝑦=522ln

Q23:

Determine the derivative of 𝑟(𝑡)=8.

  • A𝑟(𝑡)=36×8
  • B𝑟(𝑡)=882𝑡ln
  • C𝑟(𝑡)=3×88𝑡ln
  • D𝑟(𝑡)=88ln
  • E𝑟(𝑡)=6×8𝑡

Q24:

Find the derivative of the function 𝑔(𝑥)=(2𝑟𝑎+𝑛), where 𝑎, 𝑝, 𝑟, and 𝑛 are constants.

  • A𝑔(𝑥)=2𝑟𝑝(𝑎)(2𝑟𝑎+𝑛)𝑎ln
  • B𝑔(𝑥)=2𝑟𝑝(2𝑟𝑎+𝑛)𝑎
  • C𝑔(𝑥)=2𝑟𝑝(2𝑟𝑎+𝑛)
  • D𝑔(𝑥)=2𝑟𝑝(𝑎)(2𝑟𝑎+𝑛)𝑎ln
  • E𝑔(𝑥)=2𝑟𝑝(𝑎)(2𝑟𝑎+𝑛)ln

Q25:

Determine the derivative of 𝑓(𝑡)=6.

  • A𝑓(𝑡)=76𝑡6ln
  • B𝑓(𝑡)=76𝑡
  • C𝑓(𝑡)=66ln
  • D𝑓(𝑡)=6𝑡6ln
  • E𝑓(𝑡)=6𝑡6ln

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