Differentiation - Trigonometric Functions Date Period

Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Trigonometric Functions

Date________________ Period____

Differentiate each function with respect to x.

1) f ( x) = sin 2 x 3

2) y = tan 5 x 3

3) y = sec 4 x 5

4) y = csc 5 x 5

5) y = (2 x 5 + 3)cos x 2

?2 x 2 ? 5

6) y =

cos 2 x 3

7) f ( x) = sin 3 x 5

8) f ( x) = cos (?3 x 2 + 2)

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2

Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Trigonometric Functions

Date________________ Period____

Differentiate each function with respect to x.

1) f ( x) = sin 2 x 3

f ' ( x) = cos 2 x 3 ? 6 x 2

= 6 x 2 cos 2 x 3

3) y = sec 4 x 5

dy

= sec 4 x 5 ? tan 4 x 5 ? 20 x 4

dx

= 20 x 4 sec 4 x 5 ? tan 4 x 5

5) y = (2 x 5 + 3)cos x 2

dy

= (2 x 5 + 3) ? ?1sin x 2 ? 2 x + cos x 2 ? 10 x 4

dx

= 2 x(?2 x 5 sin x 2 ? 3sin x 2 + 5 x 3 cos x 2 )

7) f ( x) = sin 3 x 5

f ' ( x) = 3 ? sin 2 x 5 cos x 5 ? 5 x 4

= 15 x 4 ? sin 2 x 5 cos x 5

2) y = tan 5 x 3

dy

= sec 2 5 x 3 ? 15 x 2

dx

= 15 x 2 ? sec 2 5 x 3

4) y = csc 5 x 5

dy

= ?csc 5 x 5 ? cot 5 x 5 ? 25 x 4

dx

= ?25 x 4 csc 5 x 5 ? cot 5 x 5

?2 x 2 ? 5

6) y =

cos 2 x 3

dy cos 2 x 3 ? ?4 x ? (?2 x 2 ? 5) ? ?1sin 2 x 3 ? 6 x 2

=

dx

cos 2 2 x 3

2 x(?2cos 2 x 3 ? 6 x 3 sin 2 x 3 ? 15 xsin 2 x 3 )

=

cos 2 2 x 3

8) f ( x) = cos (?3 x 2 + 2)

2

2

f ' ( x) = ?sin (?3 x 2 + 2) ? 2(?3 x 2 + 2) ? ?6 x

2

= 12 xsin (?3 x 2 + 2) ? (?3 x 2 + 2)

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Worksheet by Kuta Software LLC

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