d
z
d
t
=
46
13
We must differentiate implicitly with respect to t
.
d
d
t
[
z
2
=
x
2
+
y
2
]
→
2
z
d
z
d
t
=
2
x
d
x
d
t
+
2
y
d
y
d
t
We know that x
=
5
and y
=
12
, so we can use the original equation to determine that z
=
13
.
We can plug in all the values that we now know:
2
(
13
)
d
z
d
t
=
2
(
5
)
2
+
2
(
12
)
3
d
z
d
t
=
46
13
Note that z
could also equal −
13
, but I am assuming that the physical restrictions behind this problem would not allow such an answer. If I am incorrect, d
z
d
t
=
±
46
13
.
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Calculo Diferencial e Integrado
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