2 4 chain rule with trig worksheet PDF

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Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Trigonometric Functions

Date________________ Period____

Differentiate each function with respect to x. 1) f (x ) = sin 2x 3

2) y = tan 5x 3

3) y = sec 4x 5

4) y = csc 5x 5

5) y = ( 2x 5 + 3)cos x2

7) f (x ) = sin 3 x 5

2

6) y =

−2 x − 5 cos 2x3

8) f (x ) = cos (−3 x 2 + 2) 2

Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Trigonometric Functions

Date________________ Period____

Differentiate each function with respect to x. 1) f (x ) = sin 2x 3 f ' (x) = cos 2 x3 ⋅ 6 x2 = 6x 2cos 2x 3

3) y = sec 4x 5 dy = sec 4 x5 ⋅ tan 4x 5 ⋅ 20x 4 dx = 20x 4 sec 4x 5 ⋅ tan 4x 5

5) y = ( 2x 5 + 3)cos x2 dy = (2x 5 + 3) ⋅ −1sin x2 ⋅ 2x + cos x 2 ⋅ 10x4 dx = 2x(−2 x 5 sin x 2 − 3sin x 2 + 5x3cos x2 )

7) f (x ) = sin 3 x 5 f ' (x) = 3 ⋅ sin 2 x 5cos x5 ⋅ 5x 4 = 15 x4 ⋅ sin2 x 5 cos x5

2) y = tan 5x 3 dy 3 2 = sec 2 5 x ⋅ 15x dx = 15 x2 ⋅ sec 2 5 x3

4) y = csc 5x 5 dy = −csc 5x 5 ⋅ cot 5x 5 ⋅ 25x 4 dx = −25x 4csc 5 x5 ⋅ cot 5x 5

2

6) y =

−2 x − 5 cos 2x3

3 2 3 2 dy cos 2 x ⋅ −4x − (−2x − 5) ⋅ −1sin 2x ⋅ 6 x = dx cos 2 2x 3 2x (−2cos 2 x3 − 6x 3sin 2x 3 − 15 xsin 2x 3 ) = cos 2 2 x 3

8) f (x ) = cos (−3 x 2 + 2) 2 2

f '( x) = −sin (−3x 2 + 2 ) ⋅ 2(−3x 2 + 2) ⋅ −6 x = 12xsin (−3x 2 + 2 ) 2 ⋅ (−3 x 2 + 2 )

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