Lesson Worksheet: Power Rule of Derivatives Mathematics • Higher Education

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.


Find the derivative of ๐‘“(๐‘ฅ)=๐‘ฅ๏Šฑ๏Šง.

  • Aโˆ’1๐‘ฅ๏Šจ
  • B1๐‘ฅ๏Šจ
  • Cโˆ’1
  • D1
  • E0


Find the derivative of ๐‘“(๐‘ฅ)=โˆš๐‘ฅ.

  • A12โˆš๐‘ฅ
  • B12โˆš๐‘ฅ
  • C๐‘ฅ2๏Žข๏Žก
  • D2๐‘ฅ3๏Žข๏Žก
  • E1โˆš๐‘ฅ


Find dd๐‘ฆ๐‘ฅ, given that ๐‘ฆ=โˆ’60.


Find the derivative of ๐‘“(๐‘ฅ)=๐‘ฅ๏Šง by first principles.

Find the derivative of ๐‘“(๐‘ฅ)=๐‘ฅ๏Šจ๏Šจ by first principles.

  • A๐‘ฅ
  • B2
  • C2๐‘ฅ๏Šจ
  • D2๐‘ฅ
  • E2๐‘ฅ๏Šฉ

Find the derivative of ๐‘“(๐‘ฅ)=๐‘ฅ๏Šฉ๏Šฉ by first principles.

  • A3๐‘ฅ๏Šจ
  • B3๐‘ฅ
  • C3๐‘ฅ๏Šฉ
  • D๐‘ฅ๏Šจ
  • E3๐‘ฅ๏Šช

By considering the pattern, what is the derivative of ๐‘“(๐‘ฅ)=๐‘ฅ๏Š?

  • Add๐‘ฅ(๐‘ฅ)=๐‘›๐‘ฅ๏Š๏Š๏Šฐ๏Šง
  • Bdd๐‘ฅ(๐‘ฅ)=๐‘›๐‘ฅ๏Š๏Š
  • Cdd๐‘ฅ(๐‘ฅ)=๐‘›๐‘ฅ๏Š๏Š๏Šฑ๏Šง
  • Ddd๐‘ฅ(๐‘ฅ)=๐‘›๐‘ฅ๏Š๏Š๏Šฑ๏Šจ
  • Edd๐‘ฅ(๐‘ฅ)=๐‘ฅ๏Š๏Š๏Šฑ๏Šง


Find dd๐‘ฆ๐‘ฅ if ๐‘ฆ=6โˆš๐‘ฅ7 .

  • A37โˆš๐‘ฅ
  • Bโˆ’37โˆš๐‘ฅ
  • C67โˆš๐‘ฅ
  • D3โˆš๐‘ฅ7


Find dd๐‘ฆ๐‘ฅ, given that ๐‘ฆ=22๐‘ฅ๏Šช.

  • A88๐‘ฅ๏Šช
  • B88๐‘ฅ๏Šซ
  • C22๐‘ฅ๏Šซ
  • D88๐‘ฅ๏Šฉ


Find dd๐‘ฆ๐‘ฅ, given that ๐‘ฆ=โˆ’8๐‘ฅโˆ’4๐‘ฅ+3๐‘ฅ+5๏Šฏ๏Šซ.

  • Aโˆ’72๐‘ฅโˆ’20๐‘ฅ+3๏Šฎ๏Šช
  • Bโˆ’72๐‘ฅโˆ’20๐‘ฅ+3๏Šฏ๏Šซ
  • Cโˆ’8๐‘ฅโˆ’4๐‘ฅ+3๏Šฎ๏Šช
  • Dโˆ’72๐‘ฅโˆ’20๐‘ฅ๏Šง๏Šฆ๏Šฌ


Given that ๐‘ฆ=15โˆ’1๐‘ฅ+13๐‘ฅ๏Šฌ๏Šจ๏Šฆ, determine ๐‘ฆโ€ฒ.

  • A1๐‘ฅ+13๐‘ฅ๏Šญ๏Šง๏Šฏ
  • B6๐‘ฅ+203๐‘ฅ๏Šฌ๏Šจ๏Šฆ
  • C6๐‘ฅ+203๐‘ฅ๏Šญ๏Šง๏Šฏ
  • D5๐‘ฅ+193๐‘ฅ๏Šญ๏Šง๏Šฏ


Given that ๐‘ฆ=3๐‘ฅ+4๐‘ฅ+๐‘ฅโˆ’2โˆš๐‘ฅ๏Šฌ๏Šช๏Šจ, find ๐‘ฆ๏Ž˜.

  • A332๐‘ฅ+14๐‘ฅ+32๐‘ฅ+๐‘ฅ๏Žจ๏Žก๏Žค๏Žก๏Ž ๏Žก๏Žข๏Žก๏Šฑ
  • B332๐‘ฅ+282๐‘ฅ+32๐‘ฅโˆ’๐‘ฅ๏Šซ๏Šฉ๏Šฑ๏Šง
  • C392๐‘ฅ+18๐‘ฅ+52๐‘ฅโˆ’๐‘ฅ32๏Žจ๏Žก๏Žค๏Žก๏Ž ๏Žก๏Šฑ
  • D332๐‘ฅ+282๐‘ฅ+32๐‘ฅ+๐‘ฅ๏Šซ๏Šฉ๏Šฑ๏Šง
  • Eโˆ’332๐‘ฅโˆ’282๐‘ฅโˆ’32๐‘ฅโˆ’๐‘ฅ๏Žจ๏Žก๏Žค๏Žก๏Ž ๏Žก๏Žข๏Žก๏Šฑ


Given that ๐‘“(๐‘ฅ)=โˆ’๐‘ฅ+๐‘š๐‘ฅ+1๏Šจ, determine ๐‘š if ๐‘“โ€ฒ(3)=1.

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