Let z(x, y) = xy where x = r cos( 40) & y = r sin(0). dy dx ar dy dz Calculate ar dz by first finding dx & and using the chain rule. ar' a0 Note: To producethe 0 symbol, type the word "theta". dz dr dz

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 20T
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Question
Let z(r, y)
xy where x =
r cos( – 40) & y =r sin(0).
dz
Calculate
dr
dz
by first finding
dx dy dx
dy
&
and using the chain rule.
ar' ər' a0
a0
Note: To producethe 0 symbol, type the word "theta".
dz
ar
dz
||
Transcribed Image Text:Let z(r, y) xy where x = r cos( – 40) & y =r sin(0). dz Calculate dr dz by first finding dx dy dx dy & and using the chain rule. ar' ər' a0 a0 Note: To producethe 0 symbol, type the word "theta". dz ar dz ||
Expert Solution
Step 1

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.

z=xy

\frac{\partial z}{\partial x}=\frac{\partial }{\partial x}\left(xy\right)

\frac{\partial z}{\partial x}= y\frac{\partial \:}{\partial \:x}\left(x\right)

\frac{\partial z}{\partial x}= y\cdot 1

\frac{\partial z}{\partial x}= y

.

z=xy

\frac{\partial z}{\partial y}=\frac{\partial }{\partial y}\left(xy\right)

\frac{\partial z}{\partial y}= x\frac{\partial \:}{\partial \:y}\left(y\right)

\frac{\partial z}{\partial y}= x \cdot 1

\frac{\partial z}{\partial y}= x

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