(a) Implicit differentiation:

The equation is $\"\"$ .

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

$\"\"$

$\"\"$ .

(b) Explicit differentiation:

Solving for y.

$\"\"$

Differentiate above function with respect to x.

$\"\"$

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

$\"\"$

$\"\"$ .

(c)

Solution for part (a) is $\"\"$ .

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

$\"\"$

Thus, the result in part (a), matches with the result in part (b).

(a) $\"\"$ .

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