Lesson Worksheet: Differentiation of Logarithmic Functions Mathematics • Higher Education

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

Q1:

Find the first derivative of the function 𝑦=ο€Ήβˆ’5π‘₯+2π‘₯lnοŠͺ.

  • Aβˆ’20π‘₯+4π‘₯(βˆ’5π‘₯+2π‘₯)οŠͺln
  • Bβˆ’20π‘₯+4π‘₯
  • C20π‘₯βˆ’4π‘₯(5π‘₯βˆ’2)
  • Dπ‘₯ο€Ή5π‘₯βˆ’220π‘₯βˆ’4

Q2:

Find dd𝑦π‘₯, given that 𝑦=(2π‘₯+7)ln.

  • A32π‘₯+7
  • B6(2π‘₯+7)ln
  • C62π‘₯+7
  • D3(2π‘₯+7)ln
  • E22π‘₯+7

Q3:

Find dd𝑦π‘₯, given that 𝑦=(4π‘₯+5)ln.

  • A284π‘₯+5
  • B28(4π‘₯+5)
  • C44π‘₯+5
  • D1(4π‘₯+5)

Q4:

Find ddοŠ©οŠ©π‘¦π‘₯, given that 𝑦=584π‘₯ln.

  • A58π‘₯
  • B5π‘₯4
  • C54π‘₯
  • Dβˆ’54π‘₯

Q5:

Given that 𝑓(π‘₯)=9π‘₯ln, find 𝑓π‘₯(οŠͺ).

  • A54π‘₯οŠͺ
  • Bβˆ’18π‘₯
  • Cβˆ’9π‘₯οŠͺ
  • Dβˆ’54π‘₯οŠͺ
  • E18π‘₯

Q6:

Find the first derivative of the function 𝑦=βˆ’7π‘₯6π‘₯οŠͺοŠͺln.

  • Aβˆ’28π‘₯ο€Ή6π‘₯ο…βˆ’76οŠͺln
  • Bβˆ’112π‘₯
  • Cβˆ’28π‘₯ο€Ήο€Ή6π‘₯+1ο…οŠ©οŠͺln
  • Dβˆ’28π‘₯ο€Ήο€Ή6π‘₯+1οŠͺοŠͺln

Q7:

Differentiate 𝑓(π‘₯)=5(5π‘₯)sinln.

  • A𝑓′(π‘₯)=25(5π‘₯)cosln
  • B𝑓′(π‘₯)=βˆ’25π‘₯(5π‘₯)cosln
  • C𝑓′(π‘₯)=βˆ’25(5π‘₯)cosln
  • D𝑓′(π‘₯)=25π‘₯(π‘₯)cosln
  • E𝑓′(π‘₯)=25π‘₯(5π‘₯)cosln

Q8:

Find dd𝑦π‘₯, given that 𝑦=4π‘₯+34π‘₯βˆ’7lnln.

  • Aβˆ’16π‘₯(4π‘₯βˆ’7)ln
  • Bβˆ’40π‘₯(4π‘₯βˆ’7)ln
  • Cβˆ’10π‘₯(4π‘₯βˆ’7)ln
  • Dβˆ’40π‘₯(4π‘₯βˆ’7)ln

Q9:

If 𝑓(π‘₯)=3(2π‘₯+4π‘₯)lnln, find 𝑓′(1).

  • A19
  • B1
  • C3
  • D9
  • E12

Q10:

Find the slope of the tangent to the curve 𝑦=βˆ’8ο€Ή7π‘₯+1log at π‘₯=βˆ’2 rounded to the nearest hundredth.

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