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partial derivative of zarctan(y/x)
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∂
∂
z
(
z
arctan
(
y
x
)
)
=
arctan
(
y
x
)
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∂
∂
z
(
z
arctan
(
y
x
)
)
=
arctan
(
y
x
)
steps
∂
∂
z
(
z
arctan
(
y
x
)
)
Treat
y
,
x
as
constants
Take
the
constant
out
:
(
a
·
f
)
′
=
a
·
f
′
=
arctan
(
y
x
)
∂
∂
z
(
z
)
Apply
the
common
derivative
:
∂
∂
z
(
z
)
=
1
=
arctan
(
y
x
)
·
1
Simplify
=
arctan
(
y
x
)
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