Use the equations to find ∂z/∂x and ∂z/∂y. x² + 4y² + 3z² = 1

Solution:

The given equation is

x² + 4y² + 3z² = 1

By differentiating z with respect to x

2x + 6z ∂z/∂x = 0

6z ∂z/∂x = -2x

∂z/∂x = -2x/6z

∂z/∂x = -x/3z

By differentiating z with respect to y

8y + 6z ∂z/∂y = 0

6z ∂z/∂y = -8y

∂z/∂y = -8y/ 6z

∂z/∂y = -4y/3z

Therefore, ∂z/∂x = -x/3z and ∂z/∂y = -4y/3z.

---

Use the equations to find ∂z/∂x and ∂z/∂y. x² + 4y² + 3z² = 1

Summary:

Using the equation x² + 4y² + 3z² = 1, ∂z/∂x = -x/3z and ∂z/∂y = -4y/3z.