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Mathematics
Mathematics
Problem
If
u
=
f
(
x
3
)
u = f(x^3)
u
=
f
(
x
3
)
,
v
=
g
(
x
2
)
v = g(x^2)
v
=
g
(
x
2
)
,
f
′
(
x
)
=
cos
x
f'(x) = \cos x
f
′
(
x
)
=
cos
x
, and
g
′
(
x
)
=
sin
x
g'(x) = \sin x
g
′
(
x
)
=
sin
x
, then
d
u
d
v
\frac{du}{dv}
d
v
d
u
is (a)
3
2
x
cos
x
3
csc
x
2
\frac{3}{2} x \cos x^3 \csc x^2
2
3
x
cos
x
3
csc
x
2
(b)
2
3
sin
x
3
sec
x
2
\frac{2}{3} \sin x^3 \sec x^2
3
2
sin
x
3
sec
x
2
(c)
tan
x
\tan x
tan
x
(d) none of these
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