100 Part I: The Questions
756. y = csc
−1
e
2x
757. y e
x
x
=
−
sec
1
Note: The derivative formula for sec
−1
 x varies,
depending on the definition used. For this problem,
use the formula d
dx
x x x
sec
−
=
−
1
2
1
1
.
758. y
x
= 4
3
arccos
759. y x
x
x
=
+ −
−
sin
1
2
1
760. y
x
x
=
+
−
−
cot
cot
1
1 1
761. y
x
x
x
=
+ +
−
tan
1
2
1
762. y
x
x
=
− +
(
)
−
tan
1
2
1
Finding Derivatives Involving
Inverse Trigonometric
Functions
750–762 Find the derivative of the given function.
750. y
x
=
−
(
)
−
2
1
1
sin
751. y
x
x
=
+
(
)
−
3
1
4
cos
752. y
x
=
−
tan
1
753. y
x
x
= −
−
1
2
1
sin
754. y
x
=
(
)
−
tan cos
1
755. y e
t
=
−
sec
1
Note: The derivative formula for sec
−1
 t varies,
depending on the definition used. For this problem,
use the formula d
dt
t t t
sec
−
=
−
1
2
1
1
.