Math 1025: Elementary Calculus
Ch. 4 Techniques of Differentiation with Applications
Derivatives of Trigonometric Functions
I.
II.
Derivatives of Trigonometric Function
1.
d
(sin x ) = cos x
dx
4.
d
(csc x ) = − csc x cot x
dx
2.
d
(cos x ) = −sin x
dx
5.
d
(sec x ) = sec x tan x
dx
3.
d
(tan x ) = sec 2 x
dx
6.
Examples
1. Show that
2.
d
( tan(x)) = sec 2 (x)
dx
y = 3cos(x 2 ) + 5x − sec(x) +
6
x
3
d
(cot x ) = − csc 2 x
dx
3.
h(y) = sin 4 (5y 3 + 6y 2 )
5.
f (t) = ln tan( t )
6.
y = ecos
7.
y=
(
2
(4 x)
cos x
1 − sin x
)
Differentiate the following examples 2 different ways
8.
9.
⎛ ex ⎞
⎟⎟
g( x ) = ⎜⎜
⎝ tan x ⎠
⎛ sin θ + cosθ ⎞
r=⎜
⎟
⎝
cos θ ⎠