Step 1:

\

The function is $\"\"$ .

\

$\"\"$ .

\

Evaluate $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Evaluate $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Formula for $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ .

\

$\"\"$ .

\

Step 2:

\

(b)

\

If $\"\"$ and $\"\"$ are increments of $\"\"$ and $\"\"$ , then the differentials of the independent variables $\"\"$ and $\"\"$ are $\"\"$ and $\"\"$ and the total differential of the dependent variable $\"\"$ is $\"\"$ .

\

$\"\"$ .

\

Apply partial derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Apply partial derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

Substitute $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Solution:

\

(a) $\"\"$ , $\"\"$ and $\"\"$ . $\"\"$ $\"\"$

\

(b) $\"\"$ .