Derivatives Of Inverse Trigonometric Functions Worksheet Page 2
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1
22
DERIVATIVES
Patterning our work after the example we can show that
1
dy
1
(1) for y = Tan
(x), we get
=
2
1 + x
dx
1
dy
1
(2) for y = Cos
(x), we get
=
√
dx
2
1
x
3. Problems
Repeat the Example for
1
(1) y = Tan
(x)
1
(2) y = Cos
(x)
Find the derivatives of the following functions
1
(1) f (x) = Sin
(2x
1).
1
2
(2) h(x) = (1 + x
)Tan
(x).
1
cos
t
(3) y =
.
t
1
(4) g(x) = Tan
(sin(x)).
x
1
x a
(5) y = Tan
+ ln
.
x+a
a
√
1
2
(6) F (t) =
1
+ Sin
t
t.
1
(7) f (x) = x sin xCos
x
1
2
(8) y = (Sin
x)
1
2
(9) y = Sin
x
1
Tan
(10) U (t) = e
t
.
Solutions to the odd numbered ones of the last 10:
2
• (1)
√
2
1 (2x 1)
1
t
cos
t
√
t 2
1
• (3)
2
t
1
(x+a)
(x
1
(
)
a)
x
a
2
1
(x+a) 2
2
x+a
• (5)
+
a
2
(
)
x
1+
x
a
a
x+a
sin x
1
1
• (7) sin x cos
x + x cos x cos
x
√
1 x
2
2x
• (9)
√
4
1 x
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