Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, , or by the subscript of the variable being considered such as  or .

For a problem like this, where we presume all variables are independent of each other, we need only consider the variable that we're taking the derivative of the function with respect to; all other variables can be treated as constants.

Taking the partial derivative of  at 

We find:

Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, , or by the subscript of the variable being considered such as  or .

For a problem like this, where we presume all variables are independent of each other, we need only consider the variable that we're taking the derivative of the function with respect to; all other variables can be treated as constants.

Taking the partial derivative of  at 

We find:

Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, , or by the subscript of the variable being considered such as  or .

For a problem like this, where we presume all variables are independent of each other, we need only consider the variable that we're taking the derivative of the function with respect to; all other variables can be treated as constants.

Taking the partial derivative of  at 

We find:

Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, , or by the subscript of the variable being considered such as  or .

For a problem like this, where we presume all variables are independent of each other, we need only consider the variable that we're taking the derivative of the function with respect to; all other variables can be treated as constants.

Knowledge of the following derivative rules will be necessary:

Trigonometric derivative: 

Note that u may represent large functions, and not just individual variables!

Taking the partial derivative of  at 

We find:

Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, , or by the subscript of the variable being considered such as  or .

For a problem like this, where we presume all variables are independent of each other, we need only consider the variable that we're taking the derivative of the function with respect to; all other variables can be treated as constants.

Knowledge of the following derivative rules will be necessary:

Derivative of a natural log: 

Note that u may represent large functions, and not just individual variables!

Taking the partial derivative of  at 

We find:

Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, , or by the subscript of the variable being considered such as  or .

For a problem like this, where we presume all variables are independent of each other, we need only consider the variable that we're taking the derivative of the function with respect to; all other variables can be treated as constants.

Taking the partial derivative of  at 

We find:

Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, , or by the subscript of the variable being considered such as  or .

For a problem like this, where we presume all variables are independent of each other, we need only consider the variable that we're taking the derivative of the function with respect to; all other variables can be treated as constants.

Taking the partial derivative of  at 

We find:

Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, , or by the subscript of the variable being considered such as  or .

For a problem like this, where we presume all variables are independent of each other, we need only consider the variable that we're taking the derivative of the function with respect to; all other variables can be treated as constants.

Knowledge of the following derivative rules will be necessary:

Derivative of a natural log: 

Note that u may represent large functions, and not just individual variables!

Taking the partial derivative of  at 

We find:

Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, , or by the subscript of the variable being considered such as  or .

For a problem like this, where we presume all variables are independent of each other, we need only consider the variable that we're taking the derivative of the function with respect to; all other variables can be treated as constants.

Knowledge of the following derivative rules will be necessary:

Derivative of an exponential: 

Note that u may represent large functions, and not just individual variables!

Taking the partial derivative of  at 

We find:

Note that for this problem, we're told to take the derivative with respect to one particular variable. This is known as taking a partial derivative; often it is denoted with the Greek character delta, , or by the subscript of the variable being considered such as  or .

For a problem like this, where we presume all variables are independent of each other, we need only consider the variable that we're taking the derivative of the function with respect to; all other variables can be treated as constants.

Taking the partial derivative of  at 

We find: