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Byju's Answer
Standard XII
Mathematics
Implicit Differentiation
If y2 = a...
Question
If
y
2
=
a
x
2
+
b
x
+
c
, then
y
3
d
2
y
d
x
2
is
A
a constant
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B
a function of x only
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C
a function of y only
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D
a function of x and y
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Solution
The correct option is
D
a function of x only
y
2
=
a
x
2
+
b
x
+
c
⇒
2
y
d
y
d
x
=
d
d
x
(
a
x
2
)
+
d
d
x
(
b
x
)
+
d
d
x
(
c
)
⇒
2
y
d
y
d
x
=
2
a
x
+
b
+
0
⇒
2
d
d
x
(
y
d
y
d
x
)
=
d
d
x
(
2
a
x
+
b
)
⇒
2
(
d
y
d
x
)
2
+
2
y
d
2
y
d
x
2
=
2
a
⇒
(
d
y
d
x
)
2
+
y
d
2
y
d
x
2
=
a
⇒
y
d
2
y
d
x
2
=
a
−
(
d
y
d
x
)
2
⇒
y
d
2
y
d
x
2
=
a
−
(
2
a
x
+
b
)
2
⇒
y
3
d
2
y
d
x
2
=
y
2
(
a
−
(
2
a
x
+
b
)
2
)
=
(
a
x
2
+
b
x
+
c
)
(
a
−
4
a
2
x
2
−
b
2
−
4
a
x
b
)
is a function of
x
only
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Similar questions
Q.
If
y
2
=
a
x
2
+
b
x
+
c
, then
y
3
.
d
2
y
d
x
2
is
Q.
If y
2
= ax
2
+ bx + c, then
y
3
d
2
y
d
x
2
is
(a) a constant
(b) a function of x only
(c) a function of y only
(d) a function of x and y
Q.
If
y
2
=
a
x
2
+
b
x
+
c
, then
y
3
.
d
2
y
d
x
2
is
Q.
If
y
2
=
a
x
2
+
b
x
+
c
, where
a
,
b
,
c
are constants, then
y
3
d
2
y
d
x
2
is equal to
Q.
If
(
a
x
2
+
b
x
+
c
)
y
+
a
′
x
2
+
b
′
x
+
c
′
=
0
, then the condition that x may be rational function of y is
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