If u=log [(x^2+y^2)/(x+y)] then find x ∂u/∂x + y ∂u/∂y .
Answers
Answered by
0
Answer:
u=log(x
3
+y
3
+z
3
−3xyz) and(
∂x
∂
+
∂y
∂
+
∂z
∂
)
2
u=
(x+y+z)
2
−k
then k=?
ANSWER
dx
du
+
dy
du
+
dz
du
=
x
3
+y
3
+z
3
−3xyz
3x
2
−3yz+3y
2
−3xz+3z
2
−3xy
=
x
3
+y
3
+z
3
−3xyz
3(x
2
+y
2
+z
2
)−3(xy+yz+xz)
dx
du
+
dy
du
+
dz
du
=
(x+y+z)
3
(
dx
d
+
dy
d
+
dz
d
)(
dx
du
+
dy
du
+
dz
du
)=(
dx
d
+
dy
d
+
dz
d
)
2
u
(x+y+z)
2
−3
+
(x+y+z)
2
−3
+
(x+y+z)
2
−3
=(
dx
d
+
dy
d
+
dz
d
)
2
u
(x+y+z)
2
−9
=(
dx
d
+
dy
d
+
dz
d
)
2
u
k=9
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