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In this lesson, we will learn how to find higher-order derivatives by implicitly differentiating equations.

Q1:

Given that π₯ + 3 π¦ = 3 2 2 , determine π¦ β² β² by implicit differentiation.

Q2:

Given that β 7 π₯ β 7 π¦ = 1 0 2 2 , determine π¦ π¦ β 1 0 7 3 β² β² .

Q3:

If β 1 0 π₯ π¦ β 5 = π₯ 2 , find π₯ οΏ π¦ π₯ ο + 2 ο½ π¦ π₯ ο d d d d 2 2 .

Q4:

Given that β 8 π₯ β 3 π₯ β 5 π¦ = 0 2 2 , find π¦ π¦ π₯ + ο½ π¦ π₯ ο d d d d 2 2 2 .

Q5:

Given that 5 π¦ = 9 π₯ 3 3 , find π¦ π¦ β² β² + 2 ( π¦ β² ) 2 .

Q6:

Given that π₯ β 3 π¦ = β 4 3 3 , find π¦ β² β² by implicit differentiation.

Q7:

Given that 2 π₯ β π₯ π¦ β π¦ = β 1 2 2 , determine π¦ β² β² by implicit differentiation.

Q8:

Given that s i n c o s π¦ + 2 π₯ = 5 , determine π¦ β² β² by implicit differentiation.

Q9:

Given that π₯ + 9 = β 2 π₯ π¦ 2 , find π₯ π¦ π₯ + 2 π¦ π₯ d d d d 2 2 .

Q10:

Let β 7 π π₯ + 5 π π₯ + π¦ = 9 π 3 2 , where π , π , and π are constants. Find π¦ οΏ π¦ π₯ ο + ο½ π¦ π₯ ο β 2 1 π π₯ d d d d 2 2 2 .

Q11:

Given that ( 6 π₯ + 7 π¦ ) = 4 7 , find d d d d 2 2 π¦ π₯ + π¦ π₯ .

Q12:

If 8 π₯ π¦ = 7 4 π₯ s i n , determine π₯ π¦ π₯ + 2 π¦ π₯ d d d d 2 2 .

Q13:

If 2 π₯ π¦ = β 1 7 5 π₯ 5 π₯ s i n c o s , find π₯ οΏ π¦ π₯ ο + 2 ο½ π¦ π₯ ο d d d d 2 2 .

Q14:

Find d d 3 3 π¦ π₯ , given that 6 π₯ + 6 π¦ = 2 5 2 2 .

Q15:

If π₯ + π₯ π¦ + π¦ = 1 2 3 , find the value of π¦ β² β² β² at π₯ = 1 .

Q16:

Suppose that π β 2 π₯ π¦ = π 2 π¦ 3 . Find π¦ β² β² when π₯ = 0 .

Q17:

Given that π π¦ + 3 π π₯ = 5 π₯ 5 π¦ 5 , determine d d π¦ π₯ at π₯ = 0 .

Q18:

Given that 9 π₯ π + π¦ π = 7 β β 5 π¦ 7 8 π₯ 5 , find d d π¦ π₯ when π₯ = 0 .

Q19:

If π = 5 π₯ β 4 π¦ π₯ π¦ , determine d d π¦ π₯ by implicit differentiation.

Q20:

Given 7 π π₯ = 8 π¦ + 5 π₯ β 4 π₯ π¦ 2 s i n , find d d π¦ π₯ at π₯ = 0 .

Q21:

Find d d π¦ π₯ by implicit differentiation if β π π₯ = 4 π₯ π¦ + 2 π₯ π¦ s i n .

Q22:

If π β² ( π₯ ) = π₯ π ( π₯ ) , and π ( β 9 ) = 6 , then determine π β² β² ( β 9 ) .

Q23:

Given that π₯ β 5 = 7 π₯ π¦ 2 , find π₯ π¦ π₯ + 2 π¦ π₯ d d d d 2 2 .

Q24:

Given that π₯ + 3 π₯ π¦ β 5 π¦ = β 2 2 2 , determine π¦ β² β² by implicit differentiation.

Q25:

Given that β 2 π¦ = π₯ 9 7 , find π¦ π¦ β² β² + 8 ( π¦ β² ) 2 .

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