Differentiate e^tantheta
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In this case, our outside function is
f(
θ
)
=
e
θ
and our inside function is
g
(
θ
)
=
tan
θ
. Note that when we compose these functions,
(
f
∘
g
)
(
θ
)
=
f
(
g
(
θ
)
)
, we get
e
tan
θ
. So we may apply the chain rule.
We will need to know the derivative of both functions.
f
′
(
θ
)
=
e
θ
g
′
(
θ
)
=
sec
2
θ
Now we use the chain rule formula:
y
′
=
f
′
(
g
(
θ
)
)
g
′
(
θ
)
=
e
tan
θ
sec
2
θ
Therefore, the derivative of the function
y
=
e
tan
θ
is
y
′
=
e
tan
θ
sec
2
θ
Hope it help u
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