Question

Q5.
Option A:
If Q = log(x² + y2 + z²), find Vo.
- 2r
p2
r
r
Option B:
Option C:
2r
l'altre
r2
Option D:
2.​

Answer 1

Step-by-step explanation:

u=f(r),r

2

=x

2

+y

2

then (

∂x

2

∂

2

u

+

∂y

2

∂

2

u

)=?

u

x

=f

′

(r)(

r

x

)

u

xx

=f

′′

(r)

r

2

x

2

+f

′

(r)

r

2

r−x⋅

r

x

u

xx

=f

′′

(r)⋅

r

2

x

2

+f

′

(r)

r

3

(r

2

−x

2

)

....(1)

Similarly,

u

yy

=f

′′

(r)

r

2

y

2

+f

′′

(r)

r

3

r

2

−y

2

.....(2)

Adding equation (1) and (2), we get

u

xx

+u

yy

=

r

2

f

′′

(r)

(x

2

+y

2

)+

r

3

f

′

(r)

[r

2

−x

2

+r

2

−y

2

]

=f

′′

(r)+

r

f

′

(r)