Question

Use the Quotient Rule to differentiate the function

Answer 1

Step 1:

(a)

The function is

Apply derivative on each side.

Quotient Rule of derivatives : .

Trigonometric reciprocal identity : .

The derivative of the function is .

Step 2:

(b)

The function is

Rewrite the expression.

Trigonometric reciprocal identity : .

The simplified expression is .

Step 3:

(c)

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 .