Solución
∂
u
∂
r
=
∂
u
∂
x
(
∂
x
∂
w
∂
w
∂
r
+
∂
x
∂
t
∂
t
∂
r
)
+
∂
u
∂
y
(
∂
y
∂
w
∂
w
∂
r
+
∂
y
∂
t
∂
t
∂
r
)
+
∂
u
∂
z
(
∂
z
∂
w
∂
w
∂
r
+
∂
z
∂
t
∂
t
∂
r
)
\frac{\partial u}{\partial r} = \frac{\partial u}{\partial x}\big(\frac{\partial x}{\partial w}\frac{\partial w}{\partial r} + \frac{\partial x}{\partial t}\frac{\partial t}{\partial r}\big)\\ + \frac{\partial u}{\partial y}\big(\frac{\partial y}{\partial w}\frac{\partial w}{\partial r} + \frac{\partial y}{\partial t}\frac{\partial t}{\partial r}\big)\\ + \frac{\partial u}{\partial z}\big(\frac{\partial z}{\partial w}\frac{\partial w}{\partial r} + \frac{\partial z}{\partial t}\frac{\partial t}{\partial r}\big)\\
∂
r
∂
u
=
∂
x
∂
u
(
∂
w
∂
x
∂
r
∂
w
+
∂
t
∂
x
∂
r
∂
t
)
+
∂
y
∂
u
(
∂
w
∂
y
∂
r
∂
w
+
∂
t
∂
y
∂
r
∂
t
)
+
∂
z
∂
u
(
∂
w
∂
z
∂
r
∂
w
+
∂
t
∂
z
∂
r
∂
t
)