Infinite Calculus - Trigonometric Differentiation

[Pages:3]Calculus

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Trigonometric Differentiation

Differentiate each function with respect to x. 1) y = sin 3x2

2) y = cos 2x3

3) y = cos 3x3

4) f (x) = sin 4x2

5) f (x) = sin x4

6) f (x) = cos 5x3

7) f (x) = sec x2

8) f (x) = csc x3

9) f (x) = tan x5

10) y = csc 2x4

11) y = sec x3

12) y = cot 2x2

13) f (x) = tan 3x3

14) y = cot 4x4

15) f (x) = (x4 - 5)sin 3x5

Worksheet by Kuta Software LLC

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16) f (x) = cos 3x3 ? (-x5 + 2) 17) f (x) = (x2 + 1)cos 3x4 18) f (x) = sin 3x3 ? (-4x5 - 5) 19) f (x) = sec x2 ? (-2x4 - 5) 20) f (x) = csc x5 ? (-5x3 + 3) 21) y = tan 2x4 ? (-x5 + 2) 22) y = cot 5x4 ? (5x5 + 3)

Worksheet by Kuta Software LLC

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Answers to Trigonometric Differentiation

1) dy = cos 3x2 ? 6x dx

2) dy = -sin 2x3 ? 6x2 dx

3) dy = -sin 3x3 ? 9x2 dx

4) f '(x) = cos 4x2 ? 8x

= 8xcos 4x2

= 6xcos 3x2

= -6x2sin 2x3

= -9x2sin 3x3

5) f '(x) = cos x4 ? 4x3 6) f '(x) = -sin 5x3 ? 15x2

7) f '(x) = sec x2tan x2 ? 2x

= 4x3cos x4

= -15x2sin 5x3

= 2xsec x2tan x2

8) f '(x) = -csc x3cot x3 ? 3x2

= -3x2csc x3cot x3

9) f '(x) = sec2 x5 ? 5x4

= 5x4sec2 x5

10) dy = -csc 2x4cot 2x4 ? 8x3 dx

= -8x3csc 2x4cot 2x4

11) dy = sec x3tan x3 ? 3x2 dx = 3x2sec x3tan x3

12) dy = -csc2 2x2 ? 4x dx = -4xcsc2 2x2

13) f '(x) = sec2 3x3 ? 9x2

= 9x2sec2 3x3

14) dy = -csc2 4x4 ? 16x3 dx

= -16x3csc2 4x4

15) f '(x) = (x4 - 5) ? cos 3x5 ? 15x4 + sin 3x5 ? 4x3 = x3(15x5cos 3x5 - 75xcos 3x5 + 4sin 3x5)

16) f '(x) = cos 3x3 ? -5x4 + (-x5 + 2) ? -sin 3x3 ? 9x2 = x2(-5x2cos 3x3 + 9x5sin 3x3 - 18sin 3x3)

17) f '(x) = (x2 + 1) ? -sin 3x4 ? 12x3 + cos 3x4 ? 2x = 2x(-6x4sin 3x4 - 6x2sin 3x4 + cos 3x4)

18) f '(x) = sin 3x3 ? -20x4 + (-4x5 - 5) ? cos 3x3 ? 9x2 = x2(-20x2sin 3x3 - 36x5cos 3x3 - 45cos 3x3)

19) f '(x) = sec x2 ? -8x3 + (-2x4 - 5) ? sec x2tan x2 ? 2x = 2xsec x2 ? (-4x2 - 2x4tan x2 - 5tan x2)

20) f '(x) = csc x5 ? -15x2 + (-5x3 + 3) ? -csc x5cot x5 ? 5x4 = 5x2csc x5 ? (-3 + 5x5cot x5 - 3x2cot x5)

21) dy = tan 2x4 ? -5x4 + (-x5 + 2) ? sec2 2x4 ? 8x3

dx

= x3(-5xtan 2x4 - 8x5sec2 2x4 + 16sec2 2x4)

22) dy = cot 5x4 ? 25x4 + (5x5 + 3) ? -csc2 5x4 ? 20x3

dx

= 5x3(5xcot 5x4 - 20x5csc2 5x4 - 12csc2 5x4)

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Worksheet by Kuta Software LLC

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