If y=2√sec(e^2x) then find dy/dx
Answers
Answered by
1
Answer:We have
d
d
x
sec
−
1
(
e
2
x
)
.
We can apply the chain rule, which states that for a function
f
(
u
)
, its derivative is
d
f
d
u
⋅
d
u
d
x
.
Here,
f
=
sec
−
1
(
u
)
, and
u
=
e
2
x
.
d
d
x
sec
−
1
(
u
)
=
1
√
u
2
√
u
2
−
1
. This is a common derivative.
d
d
x
e
2
x
. Chain rule again, here
f
=
e
u
and
x
=
2
x
. The derivative of
e
u
is
e
u
, and the derivative of
2
x
is
2
.
But here,
u
=
2
x
, and so we finally have
2
e
2
x
.
So
d
d
x
e
2
x
=
2
e
2
x
.
Now we have:
2
e
2
x
√
u
2
√
u
2
−
1
, but since
u
=
e
2
x
, we have:
2
e
2
x
√
(
e
2
x
)
2
√
(
e
2
x
)
2
−
1
2
e
2
x
e
2
x
√
(
e
4
x
)
−
1
2
√
e
4
x
−
1
, our derivative.
Step-by-step explanation:
Answered by
0
Answer:
Step-by-step explanation:
Attachments:
Similar questions