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Byju's Answer
Standard XII
Mathematics
Logarithmic Differentiation
If log 10 ...
Question
If
log
10
(
x
3
−
y
3
x
3
+
y
3
)
=
2
, then
d
y
d
x
=
A
x
y
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B
−
y
x
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C
−
x
y
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D
y
x
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Solution
The correct option is
A
y
x
Given equation is
log
10
(
x
3
−
y
3
x
3
+
y
3
)
=
2
x
3
−
y
3
x
3
+
y
3
=
100
,
applying componendo and dividendo gives,
⇒
−
x
3
y
3
=
101
99
,
⇒
x
3
y
3
=
−
101
99
,
Differentiating with respect to
x
gives,
⟹
3
x
2
y
2
⎛
⎜ ⎜ ⎜
⎝
y
−
x
d
y
d
x
y
2
⎞
⎟ ⎟ ⎟
⎠
=
0
∴
d
y
d
x
=
y
x
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0
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