differentiate 103x^6 . sec x ( 3x+2)
Answers
Answered by
4
Answer:
Note that,
y
=
sec
3
x
+
tan
2
x
sec
x
,
=
sec
x
(
sec
2
x
+
tan
2
x
)
,
=
sec
x
{
sec
2
x
+
(
sec
2
x
−
1
)
}
,
=
sec
x
(
2
sec
2
x
−
1
)
.
∴
y
=
2
sec
3
x
−
sec
x
.
∴
d
y
d
x
=
d
d
x
{
2
sec
3
x
−
sec
x
}
,
=
2
d
d
x
{
(
sec
x
)
3
}
−
d
d
x
{
sec
x
}
,
=
2
⋅
3
(
sec
x
)
2
d
d
x
{
sec
x
}
−
d
d
x
{
sec
x
}
,
=
6
sec
2
x
d
d
x
{
sec
x
}
−
d
d
x
{
sec
x
}
,
=
(
6
sec
2
x
−
1
)
d
d
x
{
sec
x
}
,
⇒
d
y
d
x
=
(
6
sec
2
x
−
1
)
sec
x
tan
x
,
or, what is the same as,
{
6
(
tan
2
x
+
1
)
−
1
}
sec
x
tan
x
=
(
6
tan
2
x
+
5
)
sec
x
tan
x
.
Enjoy Maths.!
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