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In this lesson, we will learn how to find the derivatives of positive functions by taking the natural logarithm of both sides before differentiating.

Q1:

Using logarithmic differentiation, determine the derivative of π¦ = ο π₯ + 1 2 π₯ β 2 4 .

Q2:

Use logarithmic differentiation to find the derivative of the function π¦ = 2 ( π₯ ) c o s π₯ .

Q3:

Use logarithmic differentiation to find the derivative of the function π¦ = β 5 π₯ 5 π₯ c o s .

Q4:

Use logarithmic differentiation to find the derivative of the function π¦ = 3 ( π₯ ) t a n 3 4 π₯ .

Q5:

Use logarithmic differentiation to find the derivative of the function π¦ = ( π₯ ) l n 3 π₯ c o s .

Q6:

If β 5 π¦ = 3 π₯ 6 π₯ , determine d d π¦ π₯ .

Q7:

Determine d d π¦ π₯ , given that π¦ = οΉ 5 π₯ + 1 1 ο 4 3 π₯ .

Q8:

Find d d π¦ π₯ if π¦ = οΉ 6 π₯ + 7 ο 9 8 π₯ .

Q9:

Determine d d π¦ π₯ , given that π¦ = ( 8 4 π₯ ) s i n 2 π₯ .

Q10:

Determine d d π¦ π₯ , if π¦ = ( 5 4 π₯ ) s i n t a n 4 π₯ .

Q11:

Determine d d π¦ π₯ for the function π¦ π¦ = ( 3 π₯ + 8 ) : β 2 8 π₯ c o s .

Q12:

Find d d π¦ π₯ , given that 7 π¦ = 6 π₯ s i n 6 π₯ .

Q13:

Find d d π¦ π₯ if 6 π¦ = 7 π₯ 3 5 π₯ .

Q14:

Given that π¦ = ( 8 π₯ ) l o g 4 5 π₯ t a n , find d d π¦ π₯ .

Q15:

Given that π¦ = 2 β 9 π + π₯ 9 π₯ s i n , determine d d π¦ π₯ .

Q16:

Given that π¦ = ( 3 5 π₯ ) l o g l o g 5 π₯ , find d d π¦ π₯ .

Q17:

Given π¦ = π₯ π₯ π₯ , find d d π¦ π₯ .

Q18:

If π¦ = π ο π₯ + 4 β π₯ + 4 β 6 π₯ , determine οΉ 1 6 β π₯ ο π¦ β² 2 .

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