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?
