Question

differentiate $f(x)=(2/x^{5}) - 5$.

Explanation:

Step1: Rewrite the function

Rewrite \( f(x)=\frac{2}{x^{5}} - 5\) as \( f(x)=2x^{- 5}-5\) using the rule \(\frac{a}{x^{n}}=ax^{-n}\).

Step2: Apply the power rule

The power rule is \(\frac{d}{dx}(x^{n})=nx^{n - 1}\) and \(\frac{d}{dx}(c)=0\) (where \(c\) is a constant).
For \(y = 2x^{-5}-5\), \(\frac{df(x)}{dx}=2\times(-5)x^{-5 - 1}-0\).

Step3: Simplify the expression

\(2\times(-5)x^{-6}=-10x^{-6}=-\frac{10}{x^{6}}\)

Answer:

\(-\frac{10}{x^{6}}\)