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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