Answer to Question #285938 in Classical Mechanics for RRR

Question

A=yz then it's gradient is

Answer 1

The gradient of a scalar field is given by

$${\rm grad} A=\hat i \frac{\partial A}{\partial x}+\hat j \frac{\partial A}{\partial y}+\hat k \frac{\partial A}{\partial z}$$

In our case

$${\rm grad} A=\hat i \frac{\partial (yz)}{\partial x}+\hat j \frac{\partial (yz)}{\partial y}+\hat k \frac{\partial (yz)}{\partial z}$$

$${\rm grad} A=\hat j z+\hat k y$$