differentiate $f(x)=\\frac{2}{x^{5}} - 5$
differentiate $f(x)=\\frac{2}{x^{5}} - 5$
Answer
Explanation:
Step1: Rewrite the function
Rewrite ( f(x)=\frac{2}{x^{5}} - 5) as (f(x)=2x^{- 5}-5).
Step2: Apply the power rule
The power rule is (\frac{d}{dx}(x^{n})=nx^{n - 1}). For the term (2x^{-5}), using the power rule: (\frac{d}{dx}(2x^{-5})=2\times(-5)x^{-5 - 1}=-10x^{-6}). For the constant term (-5), since (\frac{d}{dx}(C) = 0) (where (C) is a constant), (\frac{d}{dx}(-5)=0).
Step3: Combine the derivatives
(f^{\prime}(x)=\frac{d}{dx}(2x^{-5}-5)=\frac{d}{dx}(2x^{-5})-\frac{d}{dx}(5)=-10x^{-6}=-\frac{10}{x^{6}})
Answer:
(-\frac{10}{x^{6}})