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Mathematics
Problem
Calculate
d
d
x
(
x
3
x
2
+
1
)
\dfrac{d}{dx}\left(\dfrac{x^{3}}{x^{2}+1}\right)
d
x
d
(
x
2
+
1
x
3
)
. a)
3
x
2
(
x
2
+
1
)
−
2
x
3
(
x
2
+
1
)
2
\dfrac{3x^{2}(x^{2}+1)-2x^{3}}{(x^{2}+1)^{2}}
(
x
2
+
1
)
2
3
x
2
(
x
2
+
1
)
−
2
x
3
b)
3
x
4
+
2
x
3
(
x
2
+
1
)
2
\dfrac{3x^{4}+2x^{3}}{(x^{2}+1)^{2}}
(
x
2
+
1
)
2
3
x
4
+
2
x
3
c)
x
4
+
3
x
2
(
x
2
+
1
)
2
\dfrac{x^{4}+3x^{2}}{(x^{2}+1)^{2}}
(
x
2
+
1
)
2
x
4
+
3
x
2
d)
x
4
+
3
x
2
x
2
+
1
\dfrac{x^{4}+3x^{2}}{x^{2}+1}
x
2
+
1
x
4
+
3
x
2
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