Use the quotient rule to find this derivative.

Recall the quotient rule:

Begin by simplifying the expression.

Now, find the derivative using the power rule.

Recall the power rule:

Finally, substitute  for .

First, find the derivative using the power rule. 

Recall the power rule:

Now, substitute  for .

Use the power rule to find the derivative.

Recall the power rule:

First, find the derivative using the power rule:

Recall the power rule:

Now, substitute  for .

Use the quotient rule to find this derivative.

Recall the quotient rule:

This derivative requires the chain rule.

The chain rule is given by:

In this equation:

Start by applying the power rule to the parenthesis, without touching the equation inside the parenthesis.

Call this Derivative A.

To complete the derivative of the entire function, we must now take the derivative of the function inside of the parenthesis and multiply it by Derivative A.

By multiplying the  through the first parenthesis, you get the desired answer.

This can be done by using either the quotient rule or the power rule.

Power rule:

First, rewrite the equation so that  is not in the denominator:

The power rule is given by:

Then apply the power rule to the equation:

Quotient rule:

First, identify the function in the numerator and the function in the denominator:

The quotient rule is given by:

Then apply the quotient rule to the two functions:

Divergence can be viewed as a measure of the magnitude of a vector field's source or sink at a given point.

To visualize this, picture an open drain in a tub full of water; this drain may represent a 'sink,' and all of the velocities at each specific point in the tub represent the vector field. Close to the drain, the velocity will be greater than a spot farther away from the drain.

What divergence can calculate is what this velocity is at a given point. Again, the magnitude of the vector field.

We're given the function

What we will do is take the derivative of each vector element with respect to its variable 

Then sum the results together:

At the point 

Divergence can be viewed as a measure of the magnitude of a vector field's source or sink at a given point.

To visualize this, picture an open drain in a tub full of water; this drain may represent a 'sink,' and all of the velocities at each specific point in the tub represent the vector field. Close to the drain, the velocity will be greater than a spot farther away from the drain.

What divergence can calculate is what this velocity is at a given point. Again, the magnitude of the vector field.

We're given the function

What we will do is take the derivative of each vector element with respect to its variable 

Then sum the results together:

At the point