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Question
Mathematics
If y=log10 x+logx 10+logx x+log10 10 , then (dy/dx) is equal to
Q. If
y
=
l
o
g
10
x
+
l
o
g
x
10
+
l
o
g
x
x
+
l
o
g
10
10
, then
d
x
d
y
is equal to
4000
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A
x
l
o
g
e
10
1
−
x
(
l
o
g
e
x
)
2
l
o
g
e
10
B
x
l
o
g
e
10
1
−
x
l
o
g
10
e
1
C
x
l
o
g
e
10
1
+
x
(
l
o
g
e
x
)
2
l
o
g
e
10
D
None of the above
Solution:
Given,
y
=
lo
g
10
x
+
lo
g
x
10
+
lo
g
x
x
+
lo
g
10
10
⇒
y
=
lo
g
10
e
⋅
lo
g
e
x
+
l
o
g
e
x
l
o
g
e
10
+
1
+
1
On differentiating w.r.t.
x
,
we get
d
x
d
y
=
x
1
lo
g
10
e
−
x
(
l
o
g
e
x
)
2
l
o
g
e
10
=
x
l
o
g
e
10
1
−
x
(
l
o
g
e
x
)
2
l
o
g
e
10