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In this lesson, we will learn how to find the derivative of a function using the product rule.
Q1:
Find the first derivative of the function π¦ = π₯ ( 4 π₯ + 9 ) 4 9 at π₯ = β 2 .
Q2:
Find the first derivative of the function π¦ = 2 π₯ ( 8 π₯ + 7 ) 5 3 at π₯ = β 1 .
Q3:
Find the first derivative of the function π¦ = 3 π₯ ( 9 π₯ + 8 ) 5 9 at π₯ = β 1 .
Q4:
Find the first derivative of the function π¦ = 2 π₯ π 8 5 π₯ .
Q5:
Given that d d π₯ π = π π π π₯ π π₯ , find π so that π ( π₯ ) = π₯ π 2 π π₯ satisfies π β² ( 1 ) = 0 .
Q6:
Find the first derivative of the function π ( π₯ ) = οΉ 2 π₯ + π₯ β 5 ο οΌ π₯ + 3 β π₯ β 3 π₯ ο 4 2 .
Q7:
Let π ( π₯ ) = β 3 π ( π₯ ) [ β ( π₯ ) β 1 ] . If π β² ( β 4 ) = β 1 , β β² ( β 4 ) = β 9 , β ( β 4 ) = β 6 , and π ( β 4 ) = β 1 , find π β² ( β 4 ) .
Q8:
Find d d π¦ π₯ at π₯ = 2 when π¦ = οΉ π₯ + π₯ β 2 ο οΉ β 3 π₯ + 7 π₯ β 1 ο 2 2 2 5 .
Q9:
Find d d π¦ π₯ if π¦ = π π 2 π₯ 3 π₯ + 8 2 .
Q10:
Suppose that π is differentiable. What is the derivative of π₯ π ( π₯ ) 3 ?
Q11:
The product rule says that ( π π ) = π π + π π β² β² β² . Use this to derive a formula for the derivative ( π π β ) β² .
Q12:
Using the product rule, find d d π₯ ( π₯ π ) 2 β π₯ .
Q13:
Suppose that π ( 2 ) = 3 , π ( 2 ) = 5 , π β² ( 2 ) = β 1 , and π β² ( 2 ) = 6 . Evaluate ( π ( π₯ ) π ( π₯ ) ) β² β π β² ( π₯ ) π β² ( π₯ ) at π₯ = 2 .
Q14:
Find the first derivative of π¦ = ( π₯ β 5 ) ( π₯ β 2 ) 6 at ( 1 , β 4 ) .
Q15:
Find the first derivative of π ( π₯ ) = οΉ 9 π₯ β π₯ β 7 ο οΉ 7 π₯ β 8 π₯ β 7 ο 2 2 at ( β 1 , 2 4 ) .
Q16:
Find the first derivative of π ( π₯ ) = οΉ 5 π₯ + 3 π₯ β 1 ο οΉ 9 π₯ + 5 π₯ + 2 ο 2 2 at ( β 1 , 6 ) .
Q17:
Find the first derivative of π ( π₯ ) = οΉ 2 π₯ β 5 π₯ β 3 ο οΉ 5 π₯ β π₯ + 2 ο 2 2 at ( 0 , β 6 ) .
Q18:
Given π¦ π¦ = β 6 π οΉ β π₯ + 3 ο : l n 4 π₯ 2 , determine d d π¦ π₯ .
Q19:
Determine the derivative of π¦ = π π₯ β 5 π₯ 2 .
Q20:
Find the first derivative of π ( π₯ ) = 2 π₯ ( π₯ β 3 ) ( π₯ β 1 ) ( π₯ + 2 ) at ( β 1 , β 1 6 ) .
Q21:
Find the first derivative of π ( π₯ ) = π₯ ( π₯ β 1 ) ( π₯ + 4 ) ( π₯ + 6 ) at ( β 5 , β 3 0 ) .
Q22:
If π₯ = 3 π¦ π 7 9 β π¦ , find d d π₯ π¦ .
Q23:
Given π¦ = 8 π 9 π₯ + 3 π₯ 7 π₯ 3 l n , find d d π¦ π₯ .
Q24:
Differentiate π ( π§ ) = 7 4 π§ π§ 7 l o g .
Q25:
Find the first derivative of π ( π₯ ) = οΉ π₯ + 4 ο οΊ 3 π₯ β π₯ β 7 ο οΊ 3 π₯ β π₯ + 7 ο 8 at π₯ = β 1 .
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