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

Q1:

Find the first and second derivatives of the function πΊ ( π ) = 3 β π β 5 β π 5 .

Q2:

Given that π¦ = π π₯ + π π₯ ο© ο¨ , π¦ β² β² β² = β 1 8 , and ο π¦ π₯ ο£ = β 1 4 d d ο¨ ο¨ ο ο² ο¨ , find π and π .

Q3:

Find the third derivative of the function π¦ = 4 4 π₯ 2 π₯ s i n .

Q4:

If π¦ = 5 π₯ s i n , find 2 5 ο½ π¦ π₯ ο + οΏ π¦ π₯ ο d d d d 2 2 2 2 .

Q5:

True or False: ( π π ) β² β² = π β² β² π + π π β² β² .

Q6:

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

Q7:

Given that π¦ = ( π₯ β 7 ) ( 4 π₯ + 7 ) , and π§ = π₯ + 5 π₯ + 9 2 , determine d d d d 2 2 2 2 π¦ π₯ + π§ π₯ .

Q8:

Find 2 π¦ β² β² β 7 π¦ β² + 5 π¦ given π¦ = 1 + π₯ 1 + π₯ 2 + π₯ 3 + 2 3 .

Q9:

If π ( π₯ ) = π π₯ + 7 π₯ β 8 π₯ + 9 3 2 , and π β² β² ( 9 ) = β 9 , find π .

Q10:

Given that π¦ = 3 π₯ β 5 2 π₯ + 7 2 2 , determine d d 2 2 π¦ π₯ .

Q11:

Find the third derivative of the function π¦ = β 1 1 π₯ + 1 4 π₯ .

Q12:

Find the first and second derivatives of the function π ( π₯ ) = 0 . 0 0 3 π₯ β 0 . 0 4 π₯ 3 4 .

Q13:

Given that π¦ = β 4 π₯ 2 π₯ + 4 2 π₯ c o s s i n , find d d 2 2 π¦ π₯ at π₯ = 5 π 2 .

Q14:

Given that π¦ = 4 9 π₯ 5 t a n , determine π¦ β² β² .

Q15:

Find the third derivative of the function π¦ = π₯ + 5 π₯ + 3 π₯ + 2 π₯ β π₯ β 9 5 4 3 2 .

Q16:

Given that π¦ = ( β 4 π₯ + 7 ) οΉ β 7 π₯ β 4 ο 2 , determine d d 2 2 π¦ π₯ .

Q17:

Find the second derivative of the function π¦ = 5 π₯ β 4 2 π₯ β 3 at the point ( 2 , 6 ) .

Q18:

Given π¦ = β π₯ β 8 π₯ β 8 2 and d d 2 2 π¦ π₯ β 9 π + 4 = 8 . Find the value of π .

Q19:

Find d d s i n 5 1 5 1 π₯ ( π₯ ) by finding the first few derivatives and observing the pattern that occurs.

Q20:

If π¦ = π₯ 9 , find d d 8 8 π¦ π₯ .

Q21:

Determine the value of the second derivative of the function π¦ = 1 2 π₯ β 8 π₯ at ( 1 , 4 ) .

Q22:

Evaluate d d d d s e c π₯ ο β 3 π₯ + π₯ οΉ 2 π₯ β 9 π₯ ο ο‘ 3 5 .

Q23:

Given that π¦ = β 2 π₯ β 5 , determine π¦ β² β² β² .

Q24:

If π¦ βΆ π¦ = β π₯ β 1 β π₯ + 1 5 5 , find π¦ β² β² .

Q25:

Given that π¦ = 6 π₯ + 3 π₯ β 7 π₯ + 6 5 2 , determine d d 2 2 π¦ π₯ .

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