How do we implicitly differentiate xlny+ylnx=2?
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Hii
x2+xylnx
y2+xylny
−
dy
=
dx
is a special case of the
Explanation:
Implicit differentiation
for derivatives. Generally differentiation problems involve functions i.e.
. However, some functions y are written implicitly as functions of
and use chain rule. This means differentiating
, as per chain rule, we multiply it by
, but as we have to derive w.r.t.
1
dx
x
×
y
x
+
ln
+
dy
dx
dy
×
y
1
Hence differentiating xlny+ylnx=2
.
dx
×
x
+
y
ln
×
1
=
0
or
ln
y
+
y
dx
dy
x
+
x
ln
dx
dy
+
x
y
0
=
)
y
ln
+
(
x
y
−
=
dx
dy
x
)
ln
+
x
y
(
or
or
dx
dy
=
−
y
x
x
y
y
ln
+
ln
+
x
=
−
y2+xylny
x2+xylnx
x2+xylnx
y2+xylny
−
dy
=
dx
is a special case of the
Explanation:
Implicit differentiation
for derivatives. Generally differentiation problems involve functions i.e.
. However, some functions y are written implicitly as functions of
and use chain rule. This means differentiating
, as per chain rule, we multiply it by
, but as we have to derive w.r.t.
1
dx
x
×
y
x
+
ln
+
dy
dx
dy
×
y
1
Hence differentiating xlny+ylnx=2
.
dx
×
x
+
y
ln
×
1
=
0
or
ln
y
+
y
dx
dy
x
+
x
ln
dx
dy
+
x
y
0
=
)
y
ln
+
(
x
y
−
=
dx
dy
x
)
ln
+
x
y
(
or
or
dx
dy
=
−
y
x
x
y
y
ln
+
ln
+
x
=
−
y2+xylny
x2+xylnx
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0
Answer:
Step-by-step explanation:
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