Multivariable Calculus : Partial Differentiation

Example Questions

Example Question #1 : Differentiation Rules

Find .       Explanation:

In order to find , we need to take the derivative of in respect to , and treat , and as constants. We also need to remember what the derivatives of natural log, exponential functions and power functions are for single variables.

Natural Log:  Exponential Functions:  Power Functions:    Example Question #2 : Differentiation Rules

Find .       Explanation:

In order to find , we need to take the derivative of in respect to , and treat , and as constants. We also need to remember what the derivatives of natural log, exponential functions and power functions are for single variables.

Natural Log:  Exponential Functions:  Power Functions:    Example Question #3 : Differentiation Rules

Find .       Explanation:

In order to find , we need to take the derivative of in respect to , and treat , and as constants. We also need to remember what the derivatives of natural log, exponential functions and power functions are for single variables.

Natural Log:  Exponential Functions:  Power Functions:    Example Question #1 : Arc Length

Determine the length of the curve , on the interval .      Explanation:

First we need to find the tangent vector, and find its magnitude.     Now we can set up our arc length integral  Example Question #2 : Partial Differentiation

Determine the length of the curve , on the interval .      Explanation:

First we need to find the tangent vector, and find its magnitude.     Now we can set up our arc length integral   