(a)

Implicit differentiation:

The equation is $\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

(b)

Explicit differentiation:

The equation is $\"\"$ .

Solve for y.

$\"\"$

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

$\"\"$

Quotient rule of derivatives: $\"\"$ .

$\"\"$

(c)

Consider the solution in part (a): $\"\"$ .

The equation is $\"\"$ .

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

$\"\"$

$\"\"$ .

Thus, the result in part (a) and part (b) are equal.

(a) $\"\"$ .

(b) $\"\"$ and $\"\"$ .