03 - Chain Rule with Inverse Trig - Kuta Software

Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Inverse Trigonometric Functions

Date________________ Period____

Differentiate each function with respect to x. 1) y = cos −1 −5 x 3

2) y = sin −1 −2 x 2

3) y = tan −1 2 x 4

4) y = csc −1 4 x 2

5) y = (sin −1 5 x 2 )

3

6) y = sin −1 (3 x 5 + 1) 3

2

8) y = cos −1 (−2 x 3 − 3) 3

7) y = (cos −1 4 x 2 )

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Inverse Trigonometric Functions

Date________________ Period____

Differentiate each function with respect to x. 1) y = cos −1 −5 x 3 dy =− dx =

2) y = sin −1 −2 x 2 1

1 − (−5 x 3 ) 15 x 2

2

=−

1 − 25 x 6

3) y = tan −1 2 x 4

5) y = (sin −1 5 x 2 )

2

⋅ −4 x

1 − 4x4

=−

3

7) y = (cos −1 4 x 2 )

(4 x 2 ) 2 − 1

⋅ 8x

2 x 16 x 4 − 1

6) y = sin −1 (3 x 5 + 1) 3

30 x ⋅ (sin −1 5 x 1 − 25 x

1

dy =− dx 4x2

1

dy 2 = 3 ⋅ (sin −1 5 x 2 ) ⋅ dx

1 − (5 x

2 2

)

⋅ 10 x

dy = dx

2 2

)

=

4

2

dy = 2cos −1 4 x 2 ⋅ − dx =−

1 − (−2 x 2 ) 4x

4) y = csc −1 4 x 2

1 dy = ⋅ 8x3 4 dx (2 x ) 2 + 1 8x3 = 8 4x + 1

=

1

dy = dx

⋅ −15 x 2

1

2

1 − ((3 x 5 + 1) 2 45 x 4 (3 x 5 + 1) 1 − (3 x 5 + 1)

3 2

)

⋅ 3(3 x 5 + 1) ⋅ 15 x 4

6

8) y = cos −1 (−2 x 3 − 3) 3 1 1 − (4 x 2 ) 2

⋅ 8x

16 xcos −1 4 x 2 1 − 16 x 4

dy =− dx =

1

1 − ((−2 x 3 − 3) 3 ) 18 x 2 (−2 x 3 − 3) 2

2

⋅ 3(−2 x 3 − 3) 2 ⋅ −6 x 2

1 − (−2 x 3 − 3) 6

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Worksheet by Kuta Software LLC