In general:

If ,

then 

Derivative rules that will be needed here:

• Taking a derivative on a term, or using the power rule, can be done by doing the following:
• Special rule when differentiating an exponential function: , where k is a constant.

In this problem, 

Put it all together to get 

In general:

If ,

then 

Derivative rules that will be needed here:

• Taking a derivative on a term, or using the power rule, can be done by doing the following:
• When taking derivatives of sums, evaluate with the sum rule which states that the derivative of the sum is the same as the sum of the derivative of each term: 
• Special rule when differentiating an exponential function:  , where k is a constant.

In this problem, 

Put it all together to get 

In general:

If ,

then 

Derivative rules that will be needed here:

• Taking a derivative on a term, or using the power rule, can be done by doing the following:
• When taking derivatives of sums, evaluate with the sum rule which states that the derivative of the sum is the same as the sum of the derivative of each term: 
• Special rule when differentiating an exponential function:  , where k is a constant.

In this problem, 

Put it all together to get 

In general:

If ,

then 

Derivative rules that will be needed here:

• Taking a derivative on a term, or using the power rule, can be done by doing the following:
• When taking derivatives of sums, evaluate with the sum rule which states that the derivative of the sum is the same as the sum of the derivative of each term: 
• Special rule when differentiating an exponential function:  , where k is a constant.

In this problem, 

Put it all together to get 

In general:

If ,

then 

Derivative rules that will be needed here:

• Taking a derivative on a term, or using the power rule, can be done by doing the following:
• Special rule when differentiating an exponential function:  , where k is a constant.

In this problem, 

Put it all together to get 

In general:

If ,

then 

Derivative rules that will be needed here:

• Taking a derivative on a term, or using the power rule, can be done by doing the following:

In this problem, 

Put it all together to get 

In general:

If ,

then 

Derivative rules that will be needed here:

• Special rule when differentiating an exponential function:  , where k is a constant.

In this problem, 

Put it all together to get 

In general:

If ,

then 

Derivative rules that will be needed here:

• Special rule when differentiating an exponential function: , where k is a constant.

In this problem, 

Put it all together to get 

In general:

If ,

then 

Derivative rules that will be needed here:

• Taking a derivative on a term, or using the power rule, can be done by doing the following:
• When taking derivatives of sums, evaluate with the sum rule which states that the derivative of the sum is the same as the sum of the derivative of each term: 
• Special rule when differentiating an exponential function:  , where k is a constant.

In this problem, 

Use the sum rule and the power rule on each of the components.

Put it all together to get 

We obtain the cross product of the two vectors by setting up the following matrix:

Where our first row represents the unit vectors, the second row represents vector a, and the third row represents vector b. The first component of our cross product is obtained by taking the determinant of the matrix left by crossing out the row and column in which  is located. Accordingly, our second and third components are found by taking the determinant of the matrix left by crossing out the rows and columns in which    and    are located, respectively. This process gives us the following simple equation for expressing the cross product of two vectors, into which we can plug in the components of our vectors to find the cross product: