Differentiate the following trigonometric functions:

1
f(x) = sin 3x
2
f(x) = 4cos 2x
3
f(x) = 3 sin x + 4 cos x
4
y = tan 6x
5
y = -2cos 5x
6
y = sin(3x − 2)
7
g(x) = tan(3x2 + 2x)
8
y = √(cos x)
9
f(x) = cosec 2x
10
y = sec 6x
11
g(x) = -3cot x + 2sec x
12
f(x) = 5cos2x
13
y = -2sec(2x +1)
14
g(x) = cos2 4x
15
y = sin(x2)
16
f(x) = 2tan4x

17. Differentiate the following:

a
cos-1(x/4)
b
tan-1(-x/3)
c
sin-1(x + 1)
d
cosec-1(x/2)
e
tan-1 (√x)
f
tan(cos-1x)

18. Differentiate and simplify as much as possible:

y = x sin-1x + √(1 − x2)

19. Find the equation of the tangent to y = (tan-1x)2 at the point where x = 1

20. Given y = x2 − sin-1x

a. Find dy/dx

b. Verify that dy/dx = 0 when x = 1/ √2

c. Evaluate dy/dx at x = 0.5 and x = 0.8. Noting that 0.5 < 1/√2 < 0.8. What does this tell you about the point where x = 1/√2?