Worksheet: Differentiation of Exponential Functions

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

Q1:

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

  • A 2 4 𝑥 − 2 𝑒
  • B 4 𝑥 + 2 𝑒
  • C 2 4 𝑥 + 2 𝑒
  • D 2 4 𝑥 + 2

Q2:

Differentiate the function 𝑦=3𝑒−5√𝑥.

  • A 𝑦 ′ = 3 𝑒 − 5 3 𝑥
  • B 𝑦 ′ = 3 𝑒 + 5 3 𝑥
  • C 𝑦 ′ = 3 𝑒 + 5 3 𝑥
  • D 𝑦 ′ = 3 𝑒 + 5 3 𝑥
  • E 𝑦 ′ = 3 𝑒 − 5 3 𝑥

Q3:

Find the first derivative of the function 𝑦=2𝑒−5𝑒.

  • A 4 2 𝑒 − 5 𝑒
  • B 2 𝑒 − 5 𝑒 8 𝑒 + 2 5 𝑒
  • C 4 2 𝑒 − 5 𝑒 8 𝑒 + 2 5 𝑒
  • D 4 2 𝑒 − 5 𝑒 8 𝑒 + 2 5 𝑒
  • E − 4 2 𝑒 − 5 𝑒 8 𝑒 + 2 5 𝑒

Q4:

Differentiate ℎ(𝑡)=5√𝑡−𝑒.

  • A ℎ ′ ( 𝑡 ) = 5 3 √ 𝑡 − 𝑒
  • B ℎ ′ ( 𝑡 ) = 5 √ 𝑡 − 𝑒
  • C ℎ ′ ( 𝑡 ) = 5 3 √ 𝑡 − 𝑒
  • D ℎ ′ ( 𝑡 ) = 5 3 √ 𝑡 − 𝑒
  • E ℎ ′ ( 𝑡 ) = 5 3 √ 𝑡 − 𝑒

Q5:

Find dd𝑦𝑥 if 5𝑦𝑒=7𝑒.

  • A − 𝑦
  • B − 2 5 𝑦
  • C 7 5 𝑦
  • D − 2 𝑦
  • E 2 𝑦

Q6:

Determine the derivative of 𝑔(𝑥)=−5𝑒.

  • A 𝑔 ′ ( 𝑥 ) = 𝑒 3 0 𝑥 − 1 5
  • B 𝑔 ′ ( 𝑥 ) = 5 𝑒
  • C 𝑔 ′ ( 𝑥 ) = 𝑒 ( 3 0 𝑥 − 1 5 )
  • D 𝑔 ′ ( 𝑥 ) = − 5 𝑒
  • E 𝑔 ′ ( 𝑥 ) = 𝑒 1 5 𝑥 − 1 5 𝑥

Q7:

Find the derivative of the function 𝑦=5𝑥𝑒.

  • A 𝑦 = − 5 2 𝑥 𝑒 + 1
  • B 𝑦 = − 5 𝑒 ( 2 𝑥 − 1 )
  • C 𝑦 = 5 2 𝑥 𝑒 − 1
  • D 𝑦 = 1 0 𝑥 − 𝑒 𝑥
  • E 𝑦 = 5 𝑒 ( 2 𝑥 − 1 )

Q8:

Differentiate 𝑓(𝑥)=𝑒𝑥sec.

  • A 𝑓 ′ ( 𝑥 ) = 𝑒 𝑥 ( 1 − 𝑥 ) s e c t a n
  • B 𝑓 ′ ( 𝑥 ) = 𝑒 𝑥 𝑥 s e c t a n
  • C 𝑓 ′ ( 𝑥 ) = 𝑒 𝑥 ( 1 + 𝑥 ) s e c t a n
  • D 𝑓 ′ ( 𝑥 ) = 𝑥 ( 1 + 𝑒 𝑥 ) s e c t a n
  • E 𝑓 ′ ( 𝑥 ) = 𝑒 𝑥 + 𝑥 s e c t a n

Q9:

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

  • A 1 9 6 𝑥 𝑒 + 8 4 𝑒 ( 7 𝑥 + 4 )
  • B − 1 9 6 𝑥 𝑒 + 8 4 𝑒 ( 7 𝑥 + 4 )
  • C 1 9 6 𝑒 + 8 4 𝑒 ( 7 𝑥 + 4 )
  • D − 2 8 𝑥 𝑒 + 8 4 𝑒 ( 7 𝑥 + 4 )
  • E 1 9 6 𝑥 𝑒 + 8 4 𝑒 7 𝑥 + 4

Q10:

Find the first derivative of the function 𝑦=𝑒78𝑥tan.

  • A 𝑒 8 𝑥 − 8 8 𝑥 7 8 𝑥 t a n s e c t a n
  • B − 𝑒 5 8 𝑥 + 8 8 𝑥 7 8 𝑥 t a n s e c t a n
  • C 𝑒 ( 5 8 𝑥 − 8 8 𝑥 ) 7 8 𝑥 t a n s e c t a n
  • D 𝑒 5 8 𝑥 − 8 8 𝑥 7 8 𝑥 t a n s e c t a n
  • E 𝑒 5 8 𝑥 − 8 8 𝑥 7 8 𝑥 t a n s e c t a n

Q11:

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

  • A 𝑓 ′ ( 𝑧 ) = 3 𝑒 ( 4 𝑧 + 1 )
  • B 𝑓 ′ ( 𝑧 ) = 1 2 𝑒 ( 4 𝑧 + 1 )
  • C 𝑓 ′ ( 𝑧 ) = − 1 2 𝑒 4 𝑧 + 1
  • D 𝑓 ′ ( 𝑧 ) = − 3 𝑒 ( 4 𝑧 + 1 )
  • E 𝑓 ′ ( 𝑧 ) = − 1 2 𝑒 ( 4 𝑧 + 1 )

Q12:

Find the derivative of the function 𝑦=5𝑒tan.

  • A 𝑦 ′ = 1 0 𝑒 𝜃 t a n c s c
  • B 𝑦 ′ = − 1 0 𝑒 𝜃 t a n s e c
  • C 𝑦 ′ = − 1 0 𝑒 𝜃 t a n c s c
  • D 𝑦 ′ = 1 0 𝑒 𝜃 t a n t a n
  • E 𝑦 ′ = 1 0 𝑒 𝜃 t a n s e c

Q13:

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

  • A − 8 4 𝑒 7 𝑥 7 𝑥 s e c s e c t a n
  • B 1 2 𝑒 7 𝑥 7 𝑥 s e c s e c t a n
  • C 8 4 𝑒 7 𝑥 7 𝑥 s e c s e c t a n
  • D 8 4 𝑒 7 𝑥 s e c t a n
  • E 3 𝑒 s e c

Q14:

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

  • A 𝑦 = − 3 𝑒 4 𝑥 𝑒 − 1 2 √ 3 𝑥 𝑒 + 4
  • B 𝑦 = 6 𝑒 ( − 4 𝑥 + 1 ) √ 3 𝑥 𝑒 + 4
  • C 𝑦 = 3 𝑒 ( 𝑥 + 1 ) 2 √ 3 𝑥 𝑒 + 4
  • D 𝑦 = − 6 𝑒 ( − 4 𝑥 + 1 ) √ 3 𝑥 𝑒 + 4
  • E 𝑦 = 3 𝑒 ( − 4 𝑥 + 1 ) 2 √ 3 𝑥 𝑒 + 4

Q15:

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

  • A 𝑦 ′ = − 4 − 𝑒 + 5 𝑒 + 5 s i n
  • B 𝑦 ′ = − 4 0 𝑒 ( 𝑒 + 5 ) − 𝑒 + 5 𝑒 + 5 s i n
  • C 𝑦 ′ = − 4 0 𝑒 𝑒 + 5 − 𝑒 + 5 𝑒 + 5 s i n
  • D 𝑦 ′ = 4 − 𝑒 + 5 𝑒 + 5 s i n
  • E 𝑦 ′ = 4 0 𝑒 ( 𝑒 + 5 ) − 𝑒 + 5 𝑒 + 5 s i n

Q16:

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

  • A 𝑓 ′ ( 𝑡 ) = 2 𝑒 𝑒 𝑒 s i n s i n s i n s i n c o s
  • B 𝑓 ′ ( 𝑡 ) = 1 0 𝑒 𝑒 5 𝑡 𝑒 5 𝑡 s i n s i n s i n s i n s i n c o s c o s
  • C 𝑓 ′ ( 𝑡 ) = 2 0 𝑒 𝑒 5 𝑡 𝑒 5 𝑡 s i n s i n s i n s i n s i n c o s c o s
  • D 𝑓 ′ ( 𝑡 ) = − 1 0 𝑒 𝑒 5 𝑡 𝑒 5 𝑡 s i n s i n s i n s i n s i n c o s c o s
  • E 𝑓 ′ ( 𝑡 ) = − 2 0 𝑒 𝑒 5 𝑡 𝑒 5 𝑡 s i n s i n s i n s i n s i n c o s c o s

Q17:

Find 𝑓′(4), if 𝑓(𝑥)=8𝑒.

  • A 6 𝑓 ( 4 )
  • B 4 8 𝑓 ( 4 )
  • C 8 𝑓 ( 4 )
  • D 1 4 𝑓 ( 4 )

Q18:

If 𝑓(𝑥)=−5𝑒, find 𝑓(𝑥).

  • A − 1 8 𝑒
  • B − 5 𝑒
  • C 𝑒
  • D − 5 𝑒
  • E 4 5 𝑒

Q19:

Differentiate 𝑧(𝑦)=𝐴5𝑦+𝐵𝑒.

  • A d d 𝑧 𝑦 = − 3 𝐴 5 𝑦 + 3 𝐵 𝑒
  • B d d 𝑧 𝑦 = 𝐴 5 𝑦 + 𝐵 𝑒
  • C d d 𝑧 𝑦 = − 3 𝐴 5 𝑦 + 3 𝐵 𝑒
  • D d d 𝑧 𝑦 = 𝐴 5 𝑦 + 𝐵 𝑒
  • E d d 𝑧 𝑦 = − 3 𝐴 5 𝑦 + 3 𝐵 𝑒

Q20:

Find the first derivative of the function 𝑦=𝑒.

  • A − 4 𝑥 𝑒
  • B 𝑒
  • C − 3 6 𝑥 𝑒
  • D − 4 𝑥 𝑒

Q21:

If 𝑦=−3×2, determine dd𝑦𝑥.

  • A − 6 2 l n
  • B − 3 × 2 2 l n
  • C − 3 × 2 2 l n
  • D − 6 2 l n

Q22:

Find the derivative of the function 𝑦=2.

  • A 𝑦 ′ = 2 5 7 ⋅ 2 l n l n l n
  • B 𝑦 ′ = 2 ⋅ 2 l n
  • C 𝑦 ′ = 2 5 7 ⋅ 2 ⋅ 5 ⋅ 7 l n l n l n
  • D 𝑦 ′ = 7 ⋅ 2 ⋅ 5 ⋅ 7 l n
  • E 𝑦 ′ = 5 ⋅ 2 ⋅ 2 l n

Q23:

Determine the derivative of 𝑟(𝑡)=8√.

  • A 𝑟 ′ ( 𝑡 ) = 3 6 × 8 √
  • B 𝑟 ′ ( 𝑡 ) = 8 8 2 √ 𝑡 √ l n
  • C 𝑟 ′ ( 𝑡 ) = 3 × 8 8 √ 𝑡 √ l n
  • D 𝑟 ′ ( 𝑡 ) = 8 8 √ l n
  • E 𝑟 ′ ( 𝑡 ) = 6 × 8 √ 𝑡 √

Q24:

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

  • A 𝑔 ′ ( 𝑥 ) = 2 𝑟 𝑝 ( 𝑎 ) ( 2 𝑟 𝑎 + 𝑛 ) 𝑎 l n
  • B 𝑔 ′ ( 𝑥 ) = 2 𝑟 𝑝 ( 2 𝑟 𝑎 + 𝑛 ) 𝑎
  • C 𝑔 ′ ( 𝑥 ) = 2 𝑟 𝑝 ( 2 𝑟 𝑎 + 𝑛 )
  • D 𝑔 ′ ( 𝑥 ) = 2 𝑟 𝑝 ( 𝑎 ) ( 2 𝑟 𝑎 + 𝑛 ) 𝑎 l n
  • E 𝑔 ′ ( 𝑥 ) = 2 𝑟 𝑝 ( 𝑎 ) ( 2 𝑟 𝑎 + 𝑛 ) l n

Q25:

Determine the derivative of 𝑓(𝑡)=6.

  • A 𝑓 ′ ( 𝑡 ) = 7 ⋅ 6 𝑡 6 l n
  • B 𝑓 ′ ( 𝑡 ) = 7 ⋅ 6 𝑡
  • C 𝑓 ′ ( 𝑡 ) = 6 6 l n
  • D 𝑓 ′ ( 𝑡 ) = 6 𝑡 6 l n
  • E 𝑓 ′ ( 𝑡 ) = 6 𝑡 6 l n

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