Question

What is the derivative of the expression ln|x² - 1|: x³ - x^(1/4)?

(a) (x² - 1)/(x³ - x^(1/4))
(b) (2x)/(x³ - x^(1/4))
(c) 2x²/(x³ - x^(1/4))
(d) 2x/(x³ - x^(1/4)) | ln|x² - 1|

Answer 1

The derivative of the expression ln|x² - 1| is (x² - 1)/(x³ - x^(1/4)).

Step-by-step explanation:

The derivative of the expression ln|x² - 1| is found using the chain rule. Let's denote the expression inside the logarithm as u, which is |x² - 1|. Then, the derivative becomes (1/u) * du/dx.

Applying the chain rule, we find du/dx = 2x/(x² - 1).

Substituting this back into the derivative expression, we get the final result as (1/(x² - 1)) * (2x/(x² - 1)).

Therefore, the correct option is (a) (x² - 1)/(x³ - x^(1/4)).