Question

differentiate:
\frac{1}{x} \frac{1}{x^{3}} =

Explanation:

Step1: Rewrite the function

Rewrite \(\frac{1}{x}-\frac{1}{x^{3}}\) as \(x^{-1}-x^{-3}\).

Step2: Apply the power rule

The power rule for differentiation is \(\frac{d}{dx}(x^{n}) = nx^{n - 1}\).
For \(y=x^{-1}-x^{-3}\), the derivative \(y'\) is:

$$
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$$

Step3: Rewrite in fraction form

Rewrite \(-x^{-2}+3x^{-4}\) as \(-\frac{1}{x^{2}}+\frac{3}{x^{4}}\).

Answer:

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