FINDING THE DERIVATIVE OF TRIG FUNCTIONS WORKSHEET

Problem 1 :

y = cos³x

Solution

Problem 2 :

y = x³ tan 8x

Solution

Problem 3 :

y = sin² 4x

Solution

Problem 4 :

y = cos (x² + 1)

Solution

Problem 5 :

y = tan πx

Solution

Problem 6 :

y = cos √x

Solution

Problem 7 :

y = √cos 2x

Solution

Problem 8 :

y = sin4 √x

Solution

Problem 9 :

y = tan³x

Solution

Problem 10 :

y = sin²x + cos²x

Solution

Problem 11 :

y = (sin x + cos x)²

Solution

Answer Key

1)  dy/dx = -3 sin x cos² x

2) dy/dx = 3x² tan 8x + 8x³ sec² (8x)

3)  dy/dx = 4 sin 8x

4)  dy/dx = -2x sin (x² + 1)

5)  dy/dx = π sec² (πx)

6)  dy/dx = - sin (√x) / 2√x

7)  dy/dx = (sin 2x/(√cos 2x))

8)  dy/dx = (sin2 (√x))  (sin (2√x)) / √x

9)  dy/dx = 3 tan² x sec² x

10) dy/dx = 0

11)  dy/dx = 2 (cos 2x)

Problem 1 :

√x tan x

Solution

Problem 2 :

√(x tan x)

Solution

Problem 3 :

sin 2x + cos 3x

Solution

Problem 4 :

sin (4θ + π/2)

Solution

Problem 5 :

tan θ + sec θ

Solution

Problem 6 :

sin 2x cos 3x

Solution

Problem 7 :

sin (2 cos 3x)

Solution

Problem 8 :

sec³ x4

Solution

Problem 9 :

arctan (3x - 5)

Solution

Problem 10 :

arcsin (3x - 5)

Solution

Problem 11 :

2x+cosx

Solution

Problem 12 :

y = x log x

Solution

Problem 13 :

y = (sin x)²

Solution

Problem 14 :

y = sin 2x - cos 4x

Solution

Problem 15:

y = 4x sin x

Solution

Problem 16 :

y = log(x² + 1)

Solution

Problem 17:

y = ex sin x

Solution

Answer Key

1) dydx = x sec2x +tan x2x2) dydx = xsec2x + tanx2x tan x3) dydx = 2 cos 2x - 3 sin 3x4) dyd𝜃 = -4 sin𝜃5) dyd𝜃 = sec𝜃 [ tan 𝜃 + sec 𝜃] 11) ln(2) 2x+cosx (1 - sin x)12) dy/dx = 1 + log x13) dy/dx = sin 2x 14) dy/dx = 4 sin 4x + 2 cos 2x15) dy/dx = 4x cos x + 4 sin x16) dydx= 2xx2 + 117) ex [sin (x) + cos (x)]

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