Step 1:

The function is $\"\"$

Apply derivative on each side.

$\"\"$

Quotient Rule of derivatives : $\"image\"$ .

$\"\"$

Trigonometric reciprocal identity : $\"\"$ .

$\"\"$

The derivative of the function is $\"\"$ .

Step 2:

The function is $\"\"$

Rewrite the expression.

$\"\"$

Trigonometric reciprocal identity : $\"\"$ .

$\"\"$

The simplified expression is $\"\"$ .

Step 3:

The simplified function is $\"\"$ .

Apply derivative on each side.

$\"\"$

The derivative of the simplified function is $\"\"$ .

The derivative of function and the simplified function are same.

Solution :

The derivative of the function is $\"\"$ .