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In this lesson, we will learn how to find derivatives of polynomial functions.
Q1:
Given that π¦ = π₯ + π₯ + 8 π₯ 3 2 and π§ = π₯ ( π₯ β 4 ) ( π₯ β 1 ) , determine d d d d π¦ π₯ β π§ π₯ .
Q2:
Find d d π¦ π₯ , given that β 6 π₯ π¦ = 1 1 .
Q3:
Given that π¦ = 1 5 β 1 π₯ + 1 3 π₯ 6 2 0 , determine π¦ β² .
Q4:
Find d d π¦ π₯ , given that π¦ = 7 π₯ + 1 π₯ 5 6 .
Q5:
Find d d π¦ π₯ , given that π¦ = 2 2 π₯ 4 .
Q6:
Determine the first derivative of the function π¦ = 2 π₯ οΉ 9 π₯ β 3 π₯ ο + 1 0 π₯ 2 .
Q7:
Given that π¦ = ( π₯ β 1 1 ) 3 , determine ο½ π¦ π₯ ο β π¦ ( π₯ β 1 1 ) π¦ π₯ d d d d 3 .
Q8:
Evaluate d d π₯ οΎ β 3 π₯ + π₯ 9 + 6 π ο 7 9 .
Q9:
Solve π β² ( π₯ ) = 8 1 for π₯ , where π ( π₯ ) = ( 9 π₯ + 1 ) 9 .
Q10:
Find the first derivative of the function π ( π₯ ) = β 2 π₯ + 1 0 .
Q11:
Find d d π¦ π₯ , given that π¦ = ( 7 π₯ + 3 ) 4 .
Q12:
Given that π¦ = 3 π₯ π 7 β 6 , determine d d π¦ π₯ .
Q13:
Find the first derivative of the function π¦ = π₯ β π₯ 4 β 3 π₯ + 6 4 3 .
Q14:
Find the first derivative of the function π¦ = οΉ π₯ + 8 ο οΉ 3 π₯ β 8 π₯ + 6 ο 2 3 .
Q15:
Solve π β² ( π₯ ) = β 2 7 for π₯ , where π ( π₯ ) = ( β 9 π₯ β 4 ) 3 .
Q16:
Find d d π¦ π₯ , given that π¦ = β 8 π₯ β 4 π₯ + 3 π₯ + 5 9 5 .
Q17:
Given that π¦ = ( π β 5 π₯ ) 3 , and d d π¦ π₯ = β 1 5 at π₯ = β 2 , find the values of π .
Q18:
Suppose that π ( π₯ ) = ( β 2 π₯ + π ) οΉ 3 π₯ β π ο 2 and π β² ( β 1 ) = β 1 0 . Determine π .
Q19:
Evaluate d d π₯ οΉ β 3 π₯ β 4 π₯ + 5 ο 2 .
Q20:
Given that π ( π₯ ) = β π₯ + π π₯ + 1 2 , determine π if π β² ( 3 ) = 1 .
Q21:
Differentiate π ( π₯ ) = 1 2 π₯ β 1 5 π₯ + 1 8 π₯ 1 8 2 5 3 2 .
Q22:
Differentiate π ( π₯ ) = 8 π₯ β 7 π₯ β 2 2 .
Q23:
Find the first derivative of function π¦ = ( 4 β 5 π₯ ) 4 .
Q24:
Find d d π¦ π₯ if π¦ = 2 π₯ β 7 .
Q25:
Given that π¦ = β 2 5 π₯ , determine d d π¦ π₯ .
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