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Lesson Worksheet: Logarithmic Differentiation Mathematics

In this worksheet, we will practice finding the derivatives of positive functions by taking the natural logarithm of both sides before differentiating.

Q1:

Find dd𝑦𝑥 if 𝑦=6𝑥+7.

  • A86𝑥+7+54𝑥6𝑥+7ln
  • B8𝑦6𝑥+7+54𝑥6𝑥+7ln
  • C8𝑦6𝑥+7+54𝑥6𝑥+7ln
  • D8𝑦6𝑥+7+54𝑥ln

Q2:

Find dd𝑦𝑥 if 6𝑦=7𝑥.

  • A710𝑥(1𝑥)ln
  • B710𝑥
  • C710𝑥(1𝑥)ln
  • D35𝑥(1𝑥)ln
  • E710𝑥(1𝑥)ln

Q3:

Given that 𝑦=(𝑥)ln, find dd𝑦𝑥.

  • Alnlnlnln𝑥(𝑥)+1𝑥𝑥
  • Blnlnlnln𝑥(𝑥)+1𝑥
  • Clnlnlnln𝑥(𝑥)+1𝑥
  • Dln𝑥+1
  • Elnlnlnln𝑥(𝑥)+𝑥𝑥

Q4:

Determine dd𝑦𝑥 for the function 𝑦𝑦=(3𝑥+8):cos.

  • A[3𝑥+8]16(3𝑥+8)8𝑥+68𝑥3𝑥+8coslnsincos
  • B[3𝑥+8]16(3𝑥+8)8𝑥+68𝑥3𝑥+8coslnsincos
  • C[3𝑥+8]16(3𝑥+8)8𝑥68𝑥3𝑥+8coslnsincos
  • D16(3𝑥+8)8𝑥68𝑥3𝑥+8lnsincos

Q5:

Given that 𝑦=(8𝑥)logtan, find dd𝑦𝑥.

  • A(8𝑥)20(8𝑥)5𝑥+45𝑥𝑥10loglnlogsectanlntan
  • B20(8𝑥)5𝑥+45𝑥𝑥8𝑥lnlogsectanlog
  • C20(8𝑥)5𝑥+45𝑥𝑥108𝑥lnlogsectanlnlog
  • D(8𝑥)20(8𝑥)5𝑥+45𝑥𝑥108𝑥loglnlogsectanlnlogtan

Q6:

Given 𝑦=𝑥, find dd𝑦𝑥.

  • A𝑦𝑦𝑥+1𝑥𝑥+1lnlnln
  • Blnlnln𝑦𝑥+1𝑥𝑥+1
  • C𝑦𝑦1𝑥𝑥+1lnln
  • D𝑦𝑦𝑥+1𝑥+1lnlnln

Q7:

Given that 𝑦=𝑥, determine dd𝑦𝑥.

  • A2𝑥(2𝑥+𝑥)lnln
  • B2𝑥2+𝑥+1𝑥lnln
  • C2𝑥2𝑥+1𝑥lnln
  • D2𝑥2𝑥+1𝑥lnln
  • E𝑥2𝑥+2𝑥lnln

Q8:

Use logarithmic differentiation to determine the derivative of the function 𝑦=3𝑥.

  • A6𝑥(𝑥+1)ln
  • B3𝑥2𝑥+2ln
  • C2𝑥𝑥ln
  • D2(𝑥+1)ln
  • E6𝑥

Q9:

Use logarithmic differentiation to find the derivative of the function 𝑦=2(𝑥)cos.

  • A𝑦=[𝑥+𝑥𝑥][𝑥𝑥𝑥]lncoscotlncostan
  • B𝑦=𝑥𝑥𝑥lncostan
  • C𝑦=2(𝑥)[𝑥𝑥𝑥]coslncostan
  • D𝑦=2(𝑥)[𝑥𝑥𝑥]coslncoscot
  • E𝑦=2(𝑥)[𝑥+𝑥𝑥]coslncostan

Q10:

Given that 𝑦=2sin, determine dd𝑦𝑥.

  • A9𝑒+𝑥2cosln
  • B281𝑒𝑥2sincosln
  • C281𝑒+𝑥sincos
  • D281𝑒+𝑥2sincosln

This lesson includes 41 additional questions and 261 additional question variations for subscribers.

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