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Mathematics
Mathematics
Problem
Determine
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
for
y
=
x
e
x
2
sin
2
x
y=x\,e^{x^{2}}\sin 2x
y
=
x
e
x
2
sin
2
x
. a)
e
x
2
[
sin
2
x
(
1
+
x
2
)
+
2
x
cos
2
x
]
e^{x^{2}}\bigl[\sin 2x\,(1+x^{2})+2x\cos 2x\bigr]
e
x
2
[
sin
2
x
(
1
+
x
2
)
+
2
x
cos
2
x
]
b)
e
x
2
[
sin
2
x
(
1
+
2
x
2
)
+
2
x
cos
2
x
]
e^{x^{2}}\bigl[\sin 2x\,(1+2x^{2})+2x\cos 2x\bigr]
e
x
2
[
sin
2
x
(
1
+
2
x
2
)
+
2
x
cos
2
x
]
c)
e
x
2
[
sin
2
x
+
2
x
cos
2
x
]
e^{x^{2}}\bigl[\sin 2x+2x\cos 2x\bigr]
e
x
2
[
sin
2
x
+
2
x
cos
2
x
]
d)
e
x
2
[
sin
2
x
(
1
+
2
x
2
)
−
2
x
cos
2
x
]
e^{x^{2}}\bigl[\sin 2x\,(1+2x^{2})-2x\cos 2x\bigr]
e
x
2
[
sin
2
x
(
1
+
2
x
2
)
−
2
x
cos
2
x
]
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