find derivative
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Answer:
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Step-by-step explanation:
If you have a composite function F(x), then the derivative is:
F
'
(
x
)
=
f
'
(
g
(
x
)
)
(
g
'
(
x
)
)
Or, in words:
=the derivative of the outer function with the inside function left alone times the derivative of the inner function.
So let's look at your question.
y
=
tan
(
3
x
)
The outer function is tan and the inner function is
3
x
, since
3
x
is "inside" the tan. Think of it as
tan
(
u
)
where
u
=
3
x
, so the
3
x
is composed in the tan. Deriving, we get:
The derivative of the outer function (leaving the inside function alone):
d
d
x
tan
(
3
x
)
=
sec
2
(
3
x
)
The derivative of the inner function:
d
d
x
3
x
=
3
Combining, we get:
d
d
x
y
=
y
'
=
3
sec
2
(
3
x
)
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