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Mathematics
Problem
Let
R
(
x
)
=
∫
−
1
sin
(
x
2
)
e
t
3
d
t
R(x)=\displaystyle\int_{-1}^{\sin(x^{2})} e^{t^{3}}\,dt
R
(
x
)
=
∫
−
1
s
i
n
(
x
2
)
e
t
3
d
t
. What is
R
′
(
x
)
R'(x)
R
′
(
x
)
? a)
2
x
e
sin
3
(
x
2
)
2x\,e^{\sin^{3}(x^{2})}
2
x
e
s
i
n
3
(
x
2
)
b)
6
x
cos
(
x
2
)
sin
2
(
x
2
)
e
sin
3
(
x
2
)
6x\cos(x^{2})\sin^{2}(x^{2})\,e^{\sin^{3}(x^{2})}
6
x
cos
(
x
2
)
sin
2
(
x
2
)
e
s
i
n
3
(
x
2
)
c)
2
x
cos
(
x
2
)
e
sin
3
(
x
2
)
2x\cos(x^{2})\,e^{\sin^{3}(x^{2})}
2
x
cos
(
x
2
)
e
s
i
n
3
(
x
2
)
d)
2
x
cos
(
x
2
)
e
x
6
2x\cos(x^{2})\,e^{x^{6}}
2
x
cos
(
x
2
)
e
x
6
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