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UPSC NDA Math Model Paper 4
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© examsnet.com
Question : 87
Total: 120
If
y
=
ln
(
e
m
x
+
e
−
m
x
)
,
then what is
d
y
d
x
at
x
=
0
equal to?
-1
0
1
2
Validate
Solution:
Given function is
y
=
ln
(
e
m
x
+
e
−
m
x
)
Differentiating, we get
d
y
d
x
=
1
e
m
x
+
e
−
m
x
(
m
e
m
x
−
m
e
−
m
x
)
At
x
=
0
, we have
d
y
d
x
=
m
e
m
0
−
m
e
−
m
0
2
d
y
d
x
=
0
If
y
=
ln
(
e
m
x
+
e
−
m
x
)
,
d
y
d
x
=
0
at
x
=
0.
© examsnet.com
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