(1)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Difference rule of derivative : .

Constant multiple and power rule of derivative : .

Constant rule of derivative : .

Solution :

.

(2)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Sum and difference rule of derivative : .

Constant multiple and power rule of derivative : .

Constant rule of derivative : .

.

Solution :

.

(3)

Step 1:

The function is .

Apply derivative on each side with respect to x.

Sum and difference rule of derivative : .

Constant multiple and power rule of derivative : .

.

Solution :

.

(4)

Step 1:

The function is .

Simplify the function.

Apply derivative on each side with respect to t.

Sum and difference rule of derivative : .

Constant multiple and power rule of derivative : .

Constant rule of derivative : .

.

Solution :

.

(5)

Step 1:

The function is .

Simplify the function.

Apply derivative on each side with respect to x.

Difference rule of derivative : .

Constant multiple and power rule of derivative : .

.

Solution :

.

(6)

Step 1:

The function is .

Simplify the function.

Apply derivative on each side with respect to a.

Sum and difference rule of derivative : .

Constant multiple and power rule of derivative : .

Constant rule of derivative : .

.

Solution :

.