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In this lesson, we will learn how to find the first-order derivative using the chain rule.

Q1:

If π¦ = ( π§ + 1 1 ) 7 and π§ = 5 π₯ + 8 2 , find d d π¦ π₯ .

Q2:

Given that π¦ = β 6 π§ β 2 3 2 and π§ = β 4 π₯ , determine d d π¦ π₯ .

Q3:

Evaluate d d π¦ π₯ at π₯ = 2 if π¦ = β π§ 3 and π§ = 6 π₯ β 8 .

Q4:

Find d d π¦ π₯ , given that π¦ = π§ 2 and π§ = 9 π₯ + 2 2 .

Q5:

Determine d d π§ π₯ when π₯ = 1 2 if π§ = π¦ 3 + 2 π¦ + 1 3 and π¦ = β 2 π₯ + π₯ β 3 2 .

Q6:

Evaluate d d π¦ π₯ at π₯ = β 3 if π¦ = ( β 2 + π₯ ) ( β 2 β π₯ ) 4 4 .

Q7:

Evaluate d d π¦ π₯ at π₯ = 4 if π¦ = π§ β 5 π§ + 1 2 and π§ = ο ( π₯ β 3 ) 3 2 .

Q8:

Find d d π¦ π₯ , given that π¦ = ( π§ + 9 ) 3 and π§ = π₯ β 9 4 .

Q9:

Evaluate d d π¦ π₯ at π₯ = 0 if π¦ = 5 β π§ and π§ = π₯ + 1 6 π₯ + 1 .

Q10:

Evaluate d d π¦ π§ at π§ = 3 if π¦ = π₯ β 3 π₯ + 3 and π₯ = 3 π§ + 4 .

Q11:

Evaluate d d π¦ π₯ at π₯ = β 2 if π¦ = π§ + 1 π§ β 1 and π§ = π₯ β 1 π₯ + 1 .

Q12:

Evaluate d d π¦ π₯ at π₯ = 4 if π¦ = π§ + 3 π§ + 1 3 and π§ = π₯ β 1 0 π₯ β 3 .

Q13:

Given that π¦ = π§ β 8 π§ + 1 6 4 2 and π§ = 2 5 π₯ s i n , determine d d π¦ π₯ .

Q14:

Given that π¦ = β 4 π§ + 3 2 π§ s i n and π§ = β 2 π₯ + π , find d d π¦ π₯ at π₯ = 0 .

Q15:

If π¦ = ( β 8 π§ + 1 ) 3 and π§ = 1 6 2 π₯ c o s , find d d π¦ π₯ when π₯ = π 4 .

Q16:

If π¦ = ( 7 π§ + 3 ) 4 and π§ = 1 7 2 π₯ c o t , find d d π¦ π₯ at π₯ = 3 π 8 .

Q17:

Given that π¦ = π π§ 3 6 c o t and π§ = 6 β π₯ , determine d d π¦ π₯ at π₯ = 4 .

Q18:

Find d d π¦ π₯ at π = π 6 , given π₯ = 7 5 π + 3 3 π c o s c o s 6 and π¦ = 3 2 π + 7 3 π s i n s i n 6 .

Q19:

Find d d π¦ π₯ , given that π¦ = 8 π§ + 1 π§ and π₯ π§ = 9 .

Q20:

Given that π¦ = 2 π₯ β 2 2 and π₯ = π§ β 1 3 , determine d d d d π¦ π§ + 4 π₯ π§ .

Q21:

Given that π¦ = β 7 β 4 π§ and π§ = 2 π₯ t a n , determine d d π¦ π₯ at π₯ = π 8 .

Q22:

Evaluate d d π¦ π₯ at π₯ = 2 if π¦ = 2 β π§ + 9 β π§ and π§ = 2 π₯ + 1 2 .

Q23:

Given that π¦ = 8 π§ β 6 π§ β 9 3 and π§ = 3 π₯ β 2 7 π₯ , determine d d π¦ π₯ when π₯ = β 3 .

Q24:

Given that π₯ = π‘ + 1 2 and π¦ = π β 1 π‘ , find d d π¦ π₯ .

Q25:

Determine d d π¦ π₯ at π‘ = 0 , given that π₯ = ( π‘ β 2 ) ( 4 π‘ + 3 ) , and π¦ = οΉ 3 π‘ β 4 ο ( π‘ β 3 ) 2 .

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