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Kuta Software - Infinite Calculus Name___________________________________
Differentiation - Trigonometric Functions Date________________ Period____
Differentiate each function with respect to x.
( ) 3 3
1) f x = sin 2x 2) y = tan 5x
3) y = sec 4x5 4) y = csc 5x5
( 5 ) 2 2
5) y = 2x + 3 cos x −2x − 5
6) y = 3
cos 2x
( ) 3 5 2 2
7) f x = sin x ( ) ( )
8) f x = cos −3x + 2
©g p230Y183g UK8uStVa1 qSHo9fotSwyadrZeO GL2LICZ.G 3 3AClulO 2rliHgihitls5 4rde4sYeVrTvmeodM.L d ZMLaedme4 LwBibtqh4 HIhnXfNiPn1iNtuek nCuaSlVcuunleuisQ.P Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Differentiation - Trigonometric Functions Date________________ Period____
Differentiate each function with respect to x.
( ) 3 3
1) f x = sin 2x 2) y = tan 5x
'( ) 3 2
f x = cos 2x ⋅ 6x dy 2 3 2
= 6x2cos 2x3 = sec 5x ⋅ 15x
dx
= 15x2 ⋅ sec2 5x3
3) y = sec 4x5 4) y = csc 5x5
dy = sec 4x5 ⋅ tan 4x5 ⋅ 20x4 dy = −csc 5x5 ⋅ cot 5x5 ⋅ 25x4
dx dx
= 20x4sec 4x5 ⋅ tan 4x5 = −25x4csc 5x5 ⋅ cot 5x5
( 5 ) 2 2
5) y = 2x + 3 cos x −2x − 5
6) y = 3
dy cos 2x
( 5 ) 2 2 4
= 2x + 3 ⋅ −1sin x ⋅ 2x + cos x ⋅ 10x 3 ( 2 ) 3 2
dx dy cos 2x ⋅ −4x − −2x − 5 ⋅ −1sin 2x ⋅ 6x
( 5 2 2 3 2) = 3
= 2x −2x sin x − 3sin x + 5x cos x dx cos2 2x
( 3 3 3 3)
2x −2cos 2x − 6x sin 2x − 15xsin 2x
=
cos2 2x3
( ) 3 5 2 2
7) f x = sin x ( ) ( )
8) f x = cos −3x + 2
'( ) 2 5 5 4 2 2 2
f x = 3 ⋅ sin x cos x ⋅ 5x '( ) ( ) ( )
f x = −sin −3x + 2 ⋅ 2 −3x + 2 ⋅ −6x
= 15x4 ⋅ sin2 x5cos x5 ( 2 )2 ( 2 )
= 12xsin −3x + 2 ⋅ −3x + 2
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Infinite Calculus
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