Question

Find the derivative of the function f(x) = 1 - 4x - x² / (x² - 3)?

Answer 1

To find the derivative of the given function, we can use the quotient rule. The derivative of f(x) = 1 - 4x - x² / (x² - 3) is given by (2x(1 - 4x - x²) - (-4 - 2x)(x² - 3)) / (x² - 3)².

Step-by-step explanation:

To find the derivative of the function f(x) = 1 - 4x - x² / (x² - 3), we can use the quotient rule. The quotient rule states that the derivative of a fraction is equal to the denominator times the derivative of the numerator, minus the numerator times the derivative of the denominator, all divided by the squared value of the denominator. Let's use this rule to find the derivative.

1. Find the derivative of the numerator: The derivative of 1 - 4x - x² is -4 - 2x.
2. Find the derivative of the denominator: The derivative of x² - 3 is 2x.
3. Apply the quotient rule: (2x(1 - 4x - x²) - (-4 - 2x)(x² - 3)) / (x² - 3)².
4. Simplify the expression if needed.

So, the derivative of f(x) is (2x(1 - 4x - x²) - (-4 - 2x)(x² - 3)) / (x² - 3)².