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Mathematics
Mathematics
Problem
Let
y
=
x
2
sin
x
cos
x
y=x^{2}\sin x\cos x
y
=
x
2
sin
x
cos
x
. What is
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
? a)
2
x
sin
x
+
x
2
cos
x
2x\sin x+x^{2}\cos x
2
x
sin
x
+
x
2
cos
x
b)
2
x
sin
x
cos
x
+
x
2
(
cos
2
x
+
sin
2
x
)
2x\sin x\cos x+x^{2}(\cos^{2}x+\sin^{2}x)
2
x
sin
x
cos
x
+
x
2
(
cos
2
x
+
sin
2
x
)
c)
2
x
sin
x
cos
x
+
x
2
(
cos
2
x
−
sin
2
x
)
2x\sin x\cos x+x^{2}(\cos^{2}x-\sin^{2}x)
2
x
sin
x
cos
x
+
x
2
(
cos
2
x
−
sin
2
x
)
d)
x
2
(
cos
2
x
−
sin
2
x
)
x^{2}(\cos^{2}x-\sin^{2}x)
x
2
(
cos
2
x
−
sin
2
x
)
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