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Mathematics
Mathematics
Problem
The derivative of the function,
f
(
x
)
=
cos
−
1
{
1
13
(
2
cos
x
−
3
sin
x
)
}
+
sin
−
1
{
1
13
(
2
cos
x
+
3
sin
x
)
}
f(x) = \cos^{-1} \left\{ \frac{1}{\sqrt{13}} (2 \cos x - 3 \sin x) \right\} + \sin^{-1} \left\{ \frac{1}{\sqrt{13}} (2 \cos x + 3 \sin x) \right\}
f
(
x
)
=
cos
−
1
{
13
1
(
2
cos
x
−
3
sin
x
)
}
+
sin
−
1
{
13
1
(
2
cos
x
+
3
sin
x
)
}
w.r.t.
1
+
x
2
\sqrt{1+x^2}
1
+
x
2
at
x
=
3
4
x = \frac{3}{4}
x
=
4
3
is a.
3
2
\frac{3}{2}
2
3
b.
5
2
\frac{5}{2}
2
5
c.
10
3
\frac{10}{3}
3
10
d. 0
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