# Calculus 2 : Derivatives of Vectors

## Example Questions

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### Example Question #31 : Derivatives Of Vectors

Explanation:

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

### Example Question #32 : Derivatives Of Vectors

Explanation:

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

### Example Question #31 : Derivatives Of Vectors

Explanation:

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

### Example Question #32 : Derivatives Of Vectors

Explanation:

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

### Example Question #32 : Derivatives Of Vectors

Explanation:

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

### Example Question #36 : Derivatives Of Vectors

Calculate

Explanation:

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

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