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In this lesson, we will learn how to use the chain rule two or more times to find a derivative.

Q1:

Suppose π¦ = π§ 8 and π§ = β π₯ β 1 . Find d d 2 2 π¦ π₯ .

Q2:

Suppose π¦ = π§ 3 and π§ = β π₯ + 5 . Find d d 2 2 π¦ π₯ .

Q3:

Suppose π¦ = π§ 3 and π§ = β 5 π₯ β 8 . Find d d 2 2 π¦ π₯ .

Q4:

Suppose π¦ = π§ 7 and π§ = β π₯ + 4 . Find d d 2 2 π¦ π₯ .

Q5:

Suppose π¦ = π§ 6 and π§ = β π₯ β 6 . Find d d 2 2 π¦ π₯ .

Q6:

If π¦ = β 6 π§ t a n and π§ = β 2 π₯ β 3 , find d d 2 2 π¦ π₯ .

Q7:

If π¦ = β 5 π§ t a n and π§ = β π₯ β 7 , find d d 2 2 π¦ π₯ .

Q8:

If π¦ = 2 π§ β 1 3 π§ and π§ = 2 π₯ + 5 2 , determine d d 2 2 π¦ π₯ at π₯ = 0 .

Q9:

If π¦ = π§ β 1 π§ and π§ = 2 π₯ + 1 2 , determine d d 2 2 π¦ π₯ at π₯ = 0 .

Q10:

If π¦ = π§ β 2 2 π§ and π§ = 2 π₯ β 3 2 , determine d d 2 2 π¦ π₯ at π₯ = 0 .

Q11:

Given that π¦ = ( 3 π₯ + 2 ) 4 , determine π¦ β² β² β² .

Q12:

Given that π¦ = β β π§ β 8 and π§ = β 6 π₯ β 3 2 , find d d 2 2 π¦ π₯ at π₯ = β 1 .

Q13:

Given that π¦ = β 8 π§ + 9 and π§ = 6 π₯ β 6 2 , find d d 2 2 π¦ π₯ at π₯ = 1 .

Q14:

Given that π¦ = β 6 π§ + 1 and π§ = β 2 π₯ + 1 0 2 , find d d 2 2 π¦ π₯ at π₯ = β 1 .

Q15:

Determine d d s i n 3 3 2 π₯ οΊ 7 π₯ ο .

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