derivative of function

Question

. a) Find the derivative of the function f(x) = √(x + 2) using the definition of derivative

b) State the domain of the derivative.

Answer 1

Step 1 :

Definition :

The derivative of a function f  with respect to  is denoted by .

  .

Step 2 :

(a) The function is .

Find :

The derivative of a function.

Multiply numerator and denominator by .

Substitute the limit.

Step 3 :

(b) The derivative function is

The domain of a function is all values of , those makes the function mathematically correct.

The denominator of the function should not be zero and square root should not be negative number.

The domain of the derivative is .

Solution :

The domain of the derivative is .