Worksheet: Power Rule of Derivatives

In this worksheet, we will practice using the power rule of derivatives and the derivative of a sum of functions to find the derivatives of polynomials and general power functions.

Q1:

Differentiate the function 𝑓(𝑥)=𝑥73𝑥4.

  • A𝑓(𝑥)=𝑥73𝑥4𝑥
  • B𝑓(𝑥)=2𝑥73
  • C𝑓(𝑥)=𝑥73
  • D𝑓(𝑥)=2𝑥73𝑥4𝑥
  • E𝑓(𝑥)=2𝑥73𝑥4

Q2:

Given that 𝑦=𝑥+𝑥+8𝑥 and 𝑧=𝑥(𝑥4)(𝑥1), determine dddd𝑦𝑥𝑧𝑥.

  • A4𝑥4
  • B12𝑥+4
  • C12𝑥+12
  • D2𝑥4
  • E8𝑥+4

Q3:

Find dd𝑦𝑥, given that 6𝑥𝑦=11.

  • A11𝑦6𝑥
  • B116𝑥
  • C116𝑥
  • D116𝑦𝑥𝑥

Q4:

Given that 𝑦=151𝑥+13𝑥, determine 𝑦.

  • A1𝑥+13𝑥
  • B6𝑥+203𝑥
  • C6𝑥+203𝑥
  • D5𝑥+193𝑥

Q5:

Find dd𝑦𝑥, given that 𝑦=7𝑥+1𝑥.

  • A35𝑥6𝑥
  • B35𝑥6𝑥
  • C35𝑥+6𝑥
  • D35𝑥6𝑥
  • E7𝑥+1𝑥

Q6:

Find dd𝑦𝑥, given that 𝑦=22𝑥.

  • A88𝑥
  • B88𝑥
  • C22𝑥
  • D88𝑥

Q7:

Determine the first derivative of the function 𝑦=2𝑥9𝑥3𝑥+10𝑥.

  • A54𝑥12𝑥+10
  • B18𝑥6𝑥+10
  • C54𝑥12𝑥+10𝑥
  • D18𝑥6𝑥+10𝑥

Q8:

Evaluate 𝑓(3), where 𝑓(𝑥)=17𝑥+52𝑥.

Q9:

Differentiate the function 𝑓(𝑡)=6.3𝑡+5.2𝑡+7.3.

  • A𝑓(𝑡)=6.3𝑡+5.2𝑡
  • B𝑓(𝑡)=25.2𝑡+5.2𝑡
  • C𝑓(𝑡)=31.5𝑡+10.4𝑡+7.3𝑡
  • D𝑓(𝑡)=6.3𝑡+5.2𝑡+7.3𝑡
  • E𝑓(𝑡)=31.5𝑡+10.4𝑡

Q10:

Given that 𝑦=3𝑥𝑒, determine dd𝑦𝑥.

  • A21𝑥𝑒
  • B3𝑥𝑒
  • C18𝑥𝑒+21𝑥𝑒
  • D18𝑥𝑒+3𝑥𝑒

Q11:

Find dd𝑦𝑥 if 𝑦=2𝑥.

  • A2𝑥
  • B16𝑥
  • C14𝑥
  • D14𝑥

Q12:

Given that 𝑦=25𝑥, determine dd𝑦𝑥.

Q13:

Evaluate dd𝑥3𝑥+𝑥9+6𝜋.

  • A73𝑥+8𝑥
  • B73𝑥+89𝑥
  • C73𝑥+𝑥
  • D37𝑥+𝑥81
  • E73𝑥+𝑥+6

Q14:

Find the first derivative of the function 𝑓(𝑥)=2𝑥+10.

Q15:

Find the first derivative of the function 𝑦=𝑥𝑥43𝑥+6.

  • A4𝑥3𝑥43
  • B3𝑥𝑥23
  • C𝑥𝑥43
  • D4𝑥3𝑥43𝑥+6𝑥

Q16:

Find the first derivative of the function 𝑦=𝑥+83𝑥8𝑥+6.

  • A3𝑥+16𝑥+6𝑥64
  • B12𝑥+32𝑥+6𝑥64
  • C15𝑥+48𝑥+12𝑥64
  • D18𝑥+48𝑥+12𝑥64

Q17:

Find dd𝑦𝑥, given that 𝑦=8𝑥4𝑥+3𝑥+5.

  • A72𝑥20𝑥+3
  • B72𝑥20𝑥+3
  • C8𝑥4𝑥+3
  • D72𝑥20𝑥

Q18:

Evaluate dd𝑥3𝑥4𝑥+5.

  • A9𝑥4𝑥
  • B3𝑥4
  • C6𝑥4
  • D9𝑥4

Q19:

Given that 𝑓(𝑥)=𝑥+𝑚𝑥+1, determine 𝑚 if 𝑓(3)=1.

Q20:

If the function 𝑓(𝑥)=3𝑥5, find lim𝑓(𝑥+)𝑓(𝑥).

  • A27𝑥
  • B3𝑥
  • C27
  • D27𝑥
  • E27𝑥5

Q21:

Find dd𝑦𝑥 if 𝑦=6𝑥7 .

  • A37𝑥
  • B37𝑥
  • C67𝑥
  • D3𝑥7

Q22:

If 𝑦=5(2𝑥+2𝑥)cossin, find dd𝑦𝑥.

Q23:

If 𝑦=158𝑥158𝑥sincos, find dd𝑦𝑥.

  • A24016𝑥sin
  • B24016𝑥sin
  • C1516𝑥sin
  • D0
  • E1516𝑥sin

Q24:

Find dd𝑦𝑥, given that 𝑦=43𝑥.

  • A43𝑥
  • B344𝑥
  • C344𝑥
  • D344𝑥

Q25:

Find dd𝑦𝑥, given that 𝑦=3𝑥+4𝑥+67𝑥8𝑥.

  • A12𝑥+8𝑥+6+49𝑥+64𝑥
  • B9𝑥+4𝑥+56𝑥+72𝑥
  • C12𝑥+8𝑥+6+49𝑥+64𝑥
  • D3𝑥+4𝑥+7𝑥+8𝑥
  • E12𝑥+8𝑥+49𝑥+64𝑥

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