03 - Quotient Rule - homework PDF

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Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Quotient Rule

Date________________ Period____

Differentiate each function with respect to x. 1) y =

2 2x − 5 4

3) f (x ) =

5 3 4x + 4

2) f (x ) =

4) y =

5) y =

3x 4 + 2 3x 3 − 2

6) y =

7) y =

4x 5 + x 2 + 4 2 5x − 2

8) y =

2 x −5 5

4x 3 − 3x 2 4x 5 − 4

4x 5 + 2x 2 3x 4 + 5

3x 4 + 5x 3 − 5 4 2x − 4

9) y =

x3 − x2 − 3 x5 + 3

10) y =

x4 + 6 3 − 4x

−4

4x4 − 4x 2 + 5 11) y =

5

2x 3 + 3

Critical thinking question: 12) A classmate claims that classmate wrong.

f ' f' = for any functions f and g. Show an example that proves your g' g

()

Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Quotient Rule

Date________________ Period____

Differentiate each function with respect to x. 1) y =

2 2x − 5

dy

=−

dx =−

3) f (x ) =

2 ⋅ 8x 3

(2x 4 − 5) 2

5 4 x3 + 4

=−

5 ⋅ 12x 2

(4x 3 + 4 )2 15x 2 4x 6 + 8x 3 + 4

3x 4 + 2 3x 3 − 2

3 3 4 2 dy (3x − 2) ⋅ 12x − (3x + 2 ) ⋅ 9x = dx (3 x3 − 2 ) 2 9x 6 − 24x3 − 18x 2 = 9x6 − 12 x 3 + 4

7) y =

4x 5 + x 2 + 4 2 5x − 2

dy (5x 2 − 2)( 20x 4 + 2 x) − (4x 5 + x 2 + 4 ) ⋅ 10x = dx (5 x2 − 2) 2 60x 6 − 40x 4 − 44x = 25x4 − 20 x 2 + 4

2 x −5 5

f '( x) = −

16 x3 4x8 − 20 x4 + 25

f '( x) = −

5) y =

2) f (x ) =

4

=−

4) y =

2 ⋅ 5x 4

( x 5 − 5) 2 10 x 4 x 10 − 10x 5 + 25

4x 3 − 3x 2 4x 5 − 4

dy (4x 5 − 4 )(12x 2 − 6x ) − (4x 3 − 3x 2 ) ⋅ 20x 4 = dx (4x 5 − 4 )2 −8x 7 + 9x 6 − 12 x2 + 6 x = 4x 10 − 8x5 + 4

6) y =

4x 5 + 2x 2 3x 4 + 5

4 4 5 2 3 dy (3x + 5 )(20x + 4x ) − (4x + 2x ) ⋅ 12x = dx (3 x 4 + 5 )2 12x 8 − 12x5 + 100x 4 + 20x = 9x 8 + 30 x4 + 25

8) y =

3x 4 + 5x 3 − 5 4 2x − 4

dy (2x 4 − 4 )(12x 3 + 15x 2 ) − (3x 4 + 5x 3 − 5 ) ⋅ 8x 3 = dx (2x 4 − 4) 2 −5x 6 − 4x 3 − 30 x2 = 2x 8 − 8x 4 + 8

9) y =

x3 − x2 − 3 x5 + 3

dy (x 5 + 3 )(3x2 − 2x) − (x 3 − x 2 − 3 ) ⋅ 5x 4 = dx (x5 + 3)2 −2x 7 + 3x6 + 15x4 + 9x 2 − 6 x = x10 + 6x 5 + 9

10) y =

x4 + 6 3 − 4x

−4

dy (3 − 4x = dx

) ⋅ 4x 3 − ( x4 + 6 ) ⋅ 16x−5 (3 − 4 x −4)2

−4

12x 11 − 32 x7 − 96x 3 = 9x 8 − 24 x 4 + 16

4x4 − 4x 2 + 5 11) y =

5

2x 3 + 3 10 ( 2 x + 3)(16x − 8x) − (4x − 4x + 5 ) ⋅ x 3 dy = dx (2x + 3) 5 3

3

4

5 3

14

=

56 x

3

3

2

2

3

3

+ 144 x − 8 x − 72x − 50x 12x

5

3

+ 36 x + 27

3

2

8

10

2

3

Critical thinking question: 12) A classmate claims that

f ' f' = for any functions f and g. Show an example that proves your g' g

()

classmate wrong. Many answers. Ex: f = 4, g = 2x, −

2 x2

≠0

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