Directional Derivatives and the Gradient Vector: Examples

1. Find the gradient for the following equation: x^(3/2)+2*y^(1/2)

Anwser:

To find this, we must activate the VectorCalculus package:

>	with(VectorCalculus);

Then we can use the gradient command to find the gradient:

>	Gradient(x^(3/2)+2*y^(1/2),[x,y]);

2. Find the direvative of the above function in the direction <2,3>.

Anwser:

The directional derivative is the dot product of the gradient and the unit vector of the direction of travel. To find this we use the DirectionalDiff command:

2. Find the direvative of the above function in the direction <2,3>.

>	DirectionalDiff(x^(3/2)+2*y^(1/2),<2,3>,[x,y]);