(1)

Step 1:

The function is

Let  and

Substitute and in equation .

Trignometry identity: then .

Trignometric sum and difference property : .

Trignometric sum and difference property :

Substitute and in the above equation.

.

Step 2:

Differentiate implicity on each side.

Derivative of a inverse trignometry function : .

Therfore,the implicit derivative function is .

Solution :

The implicity derivative  function is .

(2)

Step 1:

The function is .         (From (1))

Solve the function  interms of  .

Differentiate on each side with respect to .

Derivative of a inverse trignometry function : .

Substitute and in the above function.

Trignometric identity : then

If then .

.

Substitute in the .

Therefore, the explicity function is .

Solution :

The explicity derivative function is .