Partial Differentiation
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Multivariable Calculus › 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
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:
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:
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:
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
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:
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:
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:
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
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