# If f(x) = 2a|3x – 9| – ax, where a is some constant not equal to zero, find f ′(3).

Algebra is the branch of mathematics, which deals with variables and expressions. It has an immense number of applications and are used to find values of various parameters and quantities.

## Answer: For f(x) = 2a|3x – 9| – ax, f'(3) does not exists.

Let's understand how we arrived at the solution.

**Explanation:**

We have f(x) = 2a|3x – 9| – ax.

Now, f'(x) = d/dx [2a × |3x - 9| - ax ], where f'(x) is the derivative of f'(x).

Using the chain rule of derivative we get,

f ' (x) = d/dx [ 2a × |3x - 9| - ax ]

f ' (x) = d/dx [ 2a × |3x - 9| ] - d/dx [ ax ]

f ' (x) = 2a × |3x-9| / (3x-9) × d/dx [ 3x - 9] - a [ Since, d/dx of |x| = |x| / x]

f ' (x) = 2a × |3x-9| / (3x-9) × 3 - a

f ' (x) = 6a × |3x-9| / (3x-9) - a

Now, to find f'(3), we substitute x = 3 in the above equation.

⇒ f'(3) = 6a|3(3) - 9| / (3(3) - 9) - a = 6a|9 - 9| / (9 - 9) - a = 6a |0| / 0 - a

Now, we arrive at a situation where the denominator is 0, which is not possible.