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Mathematics
Problem
If
y
=
tan
−
1
4
x
1
+
5
x
2
+
tan
−
1
2
+
3
x
3
−
2
x
y = \tan^{-1} \frac{4x}{1+5x^2} + \tan^{-1} \frac{2+3x}{3-2x}
y
=
tan
−
1
1
+
5
x
2
4
x
+
tan
−
1
3
−
2
x
2
+
3
x
, then
d
y
d
x
=
\frac{dy}{dx} =
d
x
d
y
=
(a)
1
1
+
25
x
2
+
2
1
+
x
2
\frac{1}{1+25x^2} + \frac{2}{1+x^2}
1
+
25
x
2
1
+
1
+
x
2
2
(b)
5
1
+
25
x
2
+
2
1
+
x
2
\frac{5}{1+25x^2} + \frac{2}{1+x^2}
1
+
25
x
2
5
+
1
+
x
2
2
(c)
5
1
+
25
x
2
\frac{5}{1+25x^2}
1
+
25
x
2
5
(d)
1
1
+
25
x
2
\frac{1}{1+25x^2}
1
+
25
x
2
1
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