find derevative of tan4
Answers
Answered by
8
Step-by-step explanation:
By using the power rule
d
d
x
[
(
u
(
x
)
)
n
]
=
n
[
u
(
x
)
]
n
−
1
, where
u
(
x
)
is a function of
x
,
and the chain rule
d
d
x
[
f
(
u
)
]
=
d
f
d
u
d
u
d
x
, where
f
=
f
(
u
(
x
)
)
.
If we rewrite
tan
4
(
x
)
as
(
tan
x
)
4
, we have that:
f
(
u
)
=
u
4
u
(
x
)
=
tan
x
As a result:
d
d
x
[
f
(
u
)
]
=
d
f
d
u
d
u
d
x
d
d
u
[
u
4
]
⋅
d
d
x
[
tan
x
]
=
4
u
3
⋅
sec
2
x
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