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03 - Chain Rule with Inverse Trig - Kuta Software
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03 - Chain Rule with Inverse Trig - Kuta Software
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Worksheet by Kuta Software LLC. Kuta Software - Infinite Calculus. Name___________________________________. Period____.
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
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