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Similar Right Triangles

dx
0
If
dx/x=dy/y
, then
2
z
=
2
x
+
2
y
=
2
x
1+
2
y
x
=
2
x
1+
2
dy
dx
=
2
x
dx
d
2
x
+d
2
y
=
2
x
dx
d
2
z
(because
d
2
x
+d
2
y
=d
2
z
, from the figure), so
dz/z=dx/x
.
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