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Byju's Answer
Standard XII
Mathematics
Properties Derived from Trigonometric Identities
Differentiate...
Question
Differentiate
sec
h
−
1
x
with respect to
x
, by first writing
x
=
sec
h
y
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Solution
Given
sec
h
−
1
x
=
y
⇒
x
=
sec
h
y
⇒
x
cosh
y
=
1
Differentiate on both sides
⇒
x
sinh
y
×
d
y
d
x
+
cos
h
y
=
0
⇒
d
y
d
x
=
−
cos
h
y
x
sin
h
y
⇒
d
y
d
x
=
−
1
x
tan
h
y
equation
→
1
tan
h
2
y
=
1
−
sec
h
2
y
⇒
tanh
y
=
√
1
−
x
2
equation
→
2
Substituting equation (2) in equation (1)
⇒
d
y
d
x
=
−
1
x
√
1
−
x
2
⇒
d
y
d
x
=
−
1
x
√
1
−
x
2
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