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In this lesson, we will learn how to find the derivatives of logarithmic functions.

Q1:

Find d d π¦ π₯ , given that π¦ = 6 6 π₯ l o g 6 .

Q2:

Find d d π¦ π₯ , given that π¦ = β 8 π₯ l o g 8 .

Q3:

Find d d π¦ π₯ , given that π¦ = ( π₯ + 7 ) l n 2 .

Q4:

Let π΄ and π΅ , respectively, be the π¦ - and π₯ -intercepts of the tangent line to π¦ = 2 5 π₯ l n at π₯ = 2 . What is the length of the segment π΄ π΅ ?

Q5:

Differentiate π ( π₯ ) = β 3 2 π₯ l n .

Q6:

Differentiate π ( π₯ ) = 5 2 π₯ l n .

Q7:

Find d d π¦ π₯ , given that π₯ 4 π¦ = 1 2 5 l n .

Q8:

Determine the equation of the tangent to the curve π¦ = π₯ + 4 π₯ 3 l n at π₯ = 1 .

Q9:

Determine the equation of the tangent to the curve π¦ = 4 π₯ β 7 π₯ 5 l n at π₯ = 1 .

Q10:

Use logarithmic differentiation to find the derivative of the function π¦ = 4 π π₯ 3 π₯ + 5 π₯ + 3 π₯ 2 2 c o s .

Q11:

Use logarithmic differentiation to find the derivative of the function π¦ = 5 π π₯ 2 π₯ + 2 π₯ + 3 5 π₯ 2 2 c o s .

Q12:

Differentiate the function πΉ ( π ) = π l n l n .

Q13:

Determine the equation of the tangent to the curve π¦ = β 2 ο» β 2 π₯ + 2 ο l n c o s at π₯ = 3 π 4 .

Q14:

Determine the equation of the tangent to the curve π¦ = β 2 ο» β β 2 π₯ + 2 ο l n c o s at π₯ = π 4 .

Q15:

Use logarithmic differentiation to find the derivative of the function π¦ = β 4 π₯ 5 π₯ s i n .

Q16:

Use logarithmic differentiation to find the derivative of the function π¦ = 2 π₯ 4 π₯ s i n .

Q17:

Use logarithmic differentiation to determine the derivative of the function π¦ = β 3 π₯ 2 π₯ .

Q18:

Use logarithmic differentiation to determine the derivative of the function π¦ = β π₯ π₯ .

Q19:

Use logarithmic differentiation to find the derivative of the function π¦ = 5 ( π₯ ) s i n 3 π₯ l n .

Q20:

Use logarithmic differentiation to find the derivative of the function π¦ = β 2 ( π₯ ) s i n 5 π₯ l n .

Q21:

Find d d 3 3 π¦ π₯ , given that π¦ = 5 8 4 π₯ l n .

Q22:

Find d d 3 3 π¦ π₯ , given that π¦ = 1 2 6 π₯ l n .

Q23:

If π¦ = β 2 π₯ + 1 6 4 π₯ 2 l n , find the value of π₯ at which the tangent to the curve is parallel to the π₯ -axis.

Q24:

If π¦ = β π₯ + 2 4 3 π₯ 3 l n , find the value of π₯ at which the tangent to the curve is parallel to the π₯ -axis.

Q25:

Use logarithmic differentiation to find the derivative of π¦ , given that π¦ = β 5 π₯ π ( π₯ + 5 ) π₯ + 2 π₯ 2 2 3 .

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