(a)

The rule is .

Consider the constant function as .

Apply derivative on each side.

.

Derivative of a constant function is .

.

Hence .

(b)

The rule is .

is a function of .

Consider the function as .

Differentiate on each side with respect to .

.

(c)

 The rule is .

Here and are the functions of .

Consider the function as .

Differentiate on each side with respect to .

.

(d)

The rule is .

Consider the function as .

Differentiate on each side with respect to .

.

(e)

 The rule is .

Consider the function as .

Differentiate on each side with respect to .

. 

(f)

The rule is .

Consider the function as .

Differentiate on each side with respect to .

.

(a)  .

(b) .

(c) .

(d) .

(e) .

(f) .