- #1

BlackMelon

- 45

- 7

- Homework Statement
- A is a function of x, y, and z. Simplify:

$$\frac{\partial^2A}{\partial x^2}+\frac{\partial^2A}{\partial y^2}$$

- Relevant Equations
- Simplify $$\frac{\partial^2A}{\partial x^2}+\frac{\partial^2A}{\partial y^2}$$

Hi there!

I would like to know if the following simplification is correct or not:

Let A be a function of x, y, and z

$$\frac{\partial^2A}{\partial x^2}+\frac{\partial^2A}{\partial y^2}$$

$$=\ \frac{\partial^2A\partial y^2+\partial^2A\partial x^2}{\partial x^2\partial y^2}$$

$$=\frac{\partial^2A\left(\partial y^2+\partial x^2\right)}{\partial x^2\partial y^2}$$

$$=\ \frac{\partial^2A\left(\partial z^2\right)}{\partial x^2\partial y^2}$$

$$=0\ \ \left(since\frac{\partial z^2}{\partial y^2}=0\right)$$

Thanks!

I would like to know if the following simplification is correct or not:

Let A be a function of x, y, and z

$$\frac{\partial^2A}{\partial x^2}+\frac{\partial^2A}{\partial y^2}$$

$$=\ \frac{\partial^2A\partial y^2+\partial^2A\partial x^2}{\partial x^2\partial y^2}$$

$$=\frac{\partial^2A\left(\partial y^2+\partial x^2\right)}{\partial x^2\partial y^2}$$

$$=\ \frac{\partial^2A\left(\partial z^2\right)}{\partial x^2\partial y^2}$$

$$=0\ \ \left(since\frac{\partial z^2}{\partial y^2}=0\right)$$

Thanks!