Question:
The derivative of y with respect to x:
The derivative of y with respect to x:
Options:
- a) depends on p only
- b) depends on q only
- c) depends on both p and q
- d) is independent of both p and q
- a) depends on p only
- b) depends on q only
- c) depends on both p and q
- d) is independent of both p and q
correct answer : d)
Explanation:
(x + y)p + q = xpyq
\ (p + q) log (x+ y) = plogx + qlogy
pq
xy
dy
dx
+
+ +
1
=
p
x
q
y
dy
dx+
pq
xy
q
y
dy
dx
+
+ -
=
p
x
pq
xy- +
+
py qy qx qy
yx y
dy
dx
+- –
+()
=
px py px qx
xx y
+- –
+()
py qx
y
dy
dx
–
= py qx
x
–
\ dy
dx
=
y
x
which is independent of both p and q.
(x + y)p + q = xpyq
\ (p + q) log (x+ y) = plogx + qlogy
pq
xy
dy
dx
+
+ +
1
=
p
x
q
y
dy
dx+
pq
xy
q
y
dy
dx
+
+ -
=
p
x
pq
xy- +
+
py qy qx qy
yx y
dy
dx
+- –
+()
=
px py px qx
xx y
+- –
+()
py qx
y
dy
dx
–
= py qx
x
–
\ dy
dx
=
y
x
which is independent of both p and q.