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UPSC NDA Math Model Paper 7
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© examsnet.com
Question : 48
Total: 120
If
y
=
√
sin
x
+
√
sin
x
+
√
sin
x
+
.
.
.
.
.
∞
then
d
y
d
x
is equal to:
cos
x
2
y
−
1
−
cos
x
2
y
−
1
sin
x
1
−
2
y
−
sin
x
1
−
2
y
Validate
Solution:
Given:
y
=
√
sin
x
+
√
sin
x
+
√
sin
x
+
.
.
.
.
.
∞
To Find:
d
y
d
x
y
=
√
sin
x
+
√
sin
x
+
√
sin
x
+
.
.
.
.
.
∞
⇒
y
=
√
sin
x
+
y
Squaring both sides, we get
⇒
y
2
=
sin
x
+
y
Differentiating with respect to
x
, we get
⇒
2
y
d
y
d
x
=
cos
x
+
d
y
d
x
⇒
2
y
d
y
d
x
−
d
y
d
x
=
cos
x
⇒
d
y
d
x
(
2
y
−
1
)
=
cos
x
∴
d
y
d
x
=
cos
x
(
2
y
−
1
)
© examsnet.com
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