find the derivative of $f(x)=6\\sqrt{x}+\\frac{8}{x^{3}}$.\ntype your answer without fractional or negative…

find the derivative of $f(x)=6\\sqrt{x}+\\frac{8}{x^{3}}$.\ntype your answer without fractional or negative exponents.\n$f(x)=\\square$\nquestion help: video 1 video 2 message instructor\nsubmit question jump to answer

find the derivative of $f(x)=6\\sqrt{x}+\\frac{8}{x^{3}}$.\ntype your answer without fractional or negative exponents.\n$f(x)=\\square$\nquestion help: video 1 video 2 message instructor\nsubmit question jump to answer

Answer

Explanation:

Step1: Rewrite the function

Rewrite ( f(x)=6\sqrt{x}+\frac{8}{x^{3}} ) as ( f(x) = 6x^{\frac{1}{2}}+8x^{- 3}).

Step2: Apply the power rule

The power rule is ((x^{n})^\prime=nx^{n - 1}). For the first term: ((6x^{\frac{1}{2}})^\prime=6\times\frac{1}{2}x^{\frac{1}{2}-1}=3x^{-\frac{1}{2}}). For the second term: ((8x^{-3})^\prime=8\times(-3)x^{-3 - 1}=-24x^{-4}).

Step3: Rewrite without negative exponents

(3x^{-\frac{1}{2}}=\frac{3}{\sqrt{x}}) and ( - 24x^{-4}=-\frac{24}{x^{4}}).

Answer:

(\frac{3}{\sqrt{x}}-\frac{24}{x^{4}})