Chapter 3 465
Figure 2 Solution for Exercise 7, Section 3.3.Figure 3 Solution for Exercise 9, Section 3.3.- See Fig. 2.
- See Fig. 3.
- By the chain rule we calculate
∂u
∂x=∂v
∂w∂w
∂x+∂v
∂z∂z
∂x=∂v
∂w+∂v
∂z,
∂^2 u
∂x^2= ∂
∂w(∂v
∂w+∂v
∂z)∂w
∂x+ ∂
∂z(∂v
∂w+∂v
∂z)∂z
∂x=∂(^2) v
∂w^2 +^2
∂^2 v
∂w∂z+
∂^2 v
∂z^2