Question

differentiate with respect to the independent variable.

$f(x)=\frac{5 - 2x^{3}}{1 + x}$

$f(x)=\square$

Explanation:

Step1: Identify the quotient rule

The quotient rule states that if \(y = \frac{u}{v}\), then \(y^\prime=\frac{u^\prime v - uv^\prime}{v^{2}}\). Here, \(u = 5-2x^{3}\), \(u^\prime=-6x^{2}\), \(v = 1 + x\), \(v^\prime=1\).

Step2: Apply the quotient rule

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Answer:

\(\frac{-4x^{3}-6x^{2}-5}{(1 + x)^{2}}\)