(1)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Sum rule of derivative : .

Constant multiple rule of derivative : .

Derivative of sine function : .

Derivative of cosine function : .

Solution :

(2)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Constant multiple rule of derivative : .

Product rule of derivatives : .

Solution :

(3)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Quotient rule of derivatives : .

Solution :

(4)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Quotient rule of derivatives : .

Solution :

(5)

Step 1:

The function is .

Apply derivative on each side with respect to t.

Sum rule of derivative : .

Product rule of derivatives : .

Solution :

(6)

Step 1:

The function is .

Apply derivative on each side with respect to t.

Quotient rule of derivatives : .

Solution :