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In this lesson, we will learn how to differentiate natural logarithmic functions without taking the limit of the function.

Q1:

Find d d π¦ π₯ , given that π¦ = ( 4 π₯ + 5 ) l n 7 .

Q2:

Find d d π¦ π₯ , given that π¦ = οΎ β 8 π₯ 7 π₯ β 3 ο l n 2 .

Q3:

A factoryβs production of π¦ units in π‘ days is governed by the relation π¦ = 4 0 0 οΉ 1 0 β π ο β 0 . 8 π‘ . What is the rate of change of production with respect to time on the fifth day?

Q4:

Find the first derivative of the function π¦ = οΉ β 5 π₯ + 2 π₯ ο l n 4 2 .

Q5:

Find the first derivative of the function π¦ = β 7 π₯ 6 π₯ 4 4 l n .

Q6:

Find d d π¦ π₯ , given that π¦ = 9 π₯ 9 π₯ l n .

Q7:

Find d d π¦ π₯ , given that π¦ = 4 π₯ + 3 4 π₯ β 7 l n l n .

Q8:

Differentiate the function π» ( π§ ) = ο π β π§ π + π§ l n 2 2 2 2 .

Q9:

Find d d π¦ π₯ , given that π¦ = 3 π₯ 3 π₯ 6 3 l n .

Q10:

If π ( π₯ ) = 3 ( 2 π₯ + 4 π₯ ) l n l n , find π β² ( 1 ) .

Q11:

Given that π ( π₯ ) = οΊ π₯ ο c o s l n 2 , determine π β² ( 1 ) .

Q12:

Differentiate π¦ = β 5 | 5 π₯ β 5 π₯ + 3 | l n 3 .

Q13:

Differentiate π ( π₯ ) = β 5 β π₯ + 4 l n , and determine its domain.

Q14:

Differentiate πΉ ( π‘ ) = β 4 ( π‘ ) 2 π‘ l n s i n 2 .

Q15:

Given that π¦ = β 3 4 ( 7 π₯ + 7 π₯ ) l n t a n s e c , determine d d π¦ π₯ .

Q16:

Given that π¦ = 8 ( ( 9 π₯ ) ) l n l n l n , find d d π¦ π₯ .

Q17:

Differentiate π ( π₯ ) = 5 ( 5 π₯ ) s i n l n .

Q18:

Differentiate π ( π₯ ) = 5 οΊ 2 π₯ ο l n s i n 2 .

Q19:

Differentiate the function π¦ = [ ( π π₯ + π ) ] t a n l n .

Q20:

Determine d d π¦ π₯ , given that π¦ π¦ = οΌ β 1 4 π₯ β 7 ο : l n 5 .

Q21:

Differentiate π ( π₯ ) = β οΉ π₯ + 4 π₯ ο l n 2 , and determine its domain.

Q22:

Differentiate , and determine its domain.

Q23:

Differentiate π ( π£ ) = 2 π£ 5 π£ β 3 l n .

Q24:

Determine the first derivative of π¦ = β π + 2 π₯ π₯ 4 l n 8 .

Q25:

Differentiate π ( π‘ ) = β 4 π‘ β 9 l n .

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