Question

If $ f(x) = \frac{\sqrt{x^4}}{\sqrt{x^2}} $, find $ f'(27) $.

• A. \( 2 \times 27 \)
• B. \( 3 \times 27^2 \)
• C. \( 27 \)
• D. \( 54 \)

Hint:

To simplify functions involving square roots and powers, always simplify the expression first and then differentiate. This can help avoid unnecessary complications during differentiation.

Answer 1

The Correct Option is D

We are given: \[ f(x) = \frac{\sqrt{x^4}}{\sqrt{x^2}} = \frac{x^2}{x} = x \] So, \( f(x) = x \), and the derivative \( f'(x) \) is: \[ f'(x) = 1 \] Thus: \[ f'(27) = 1 \]