How do you find f ' if f(x)=sin(1x2)?
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Answers
Answered by
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Use
d
d
x
(
sin
x
)
=
cos
x
together with the chain rule to get:
d
d
x
sin
u
=
cos
u
⋅
d
u
d
x
In this case,
u
=
1
x
2
=
x
−
2
,
so
d
u
d
x
=
−
2
x
−
3
=
−
2
x
3
Putting this together, we get:
f
'
(
x
)
=
cos
(
1
x
2
)
⋅
d
d
x
(
1
x
2
)
=
cos
(
1
x
2
)
−
2
x
3
which is better written:
f
'
(
x
)
=
−
2
x
3
cos
(
1
x
2
)
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