Question
Asked Sep 30, 2019
3 views

Show that

(∂z/∂x)2 + (∂z/∂y)2 = (∂z/∂r)2 + (1/r2) (∂z/∂θ)2

check_circle

Expert Answer

Step 1

The equation to be proved is,

2
2
ôz
+
2
ôz
Oz
2
ax
help_outline

Image Transcriptionclose

2 2 ôz + 2 ôz Oz 2 ax

fullscreen
Step 2

Consider z = f (x,y) and the partial der...

д2 дх д2 ду
дх дr ду дr
Oz
ôz
(sin e)
..1)
(cos0)
дх
OzOx
до дх д0 ду д0
дz
ôz
(rcos0)
(rsin0)
axc
..(2)
help_outline

Image Transcriptionclose

д2 дх д2 ду дх дr ду дr Oz ôz (sin e) ..1) (cos0) дх OzOx до дх д0 ду д0 дz ôz (rcos0) (rsin0) axc ..(2)

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative