Find the derivative of the function (f(x) = frac{4x^3 - 9x^2 + 2x - 1}{sqrt{x}})

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Step:1 ：First, rewrite the function as (f(x) = 4x^{frac{5}{2}} - 9x^{frac{3}{2}} + 2x^{frac{1}{2}} - x^{-frac{1}{2}})Step:2 ：Apply the power rule to find the derivative of each term: (f&#x27;(x) = frac{5}{2} cdot 4x^{frac{5}{2} - 1} - frac{3}{2} cdot 9x^{frac{3}{2} - 1} + frac{1}{2} cdot 2x^{frac{1}{2} - 1} + frac{1}{2} cdot x^{-frac{1}{2} - 1})Step:3 ：Simplify to find the derivative: (f&#x27;(x) = 10x^2 - frac{27}{2}x + sqrt{x} - frac{1}{2sqrt{x}})

Answer

Step: 1 ：First, rewrite the function as (f(x) = 4x^{frac{5}{2}} - 9x^{frac{3}{2}} + 2x^{frac{1}{2}} - x^{-frac{1}{2}})Step: 2 ：Apply the power rule to find the derivative of each term: (f&#x27;(x) = frac{5}{2} cdot 4x^{frac{5}{2} - 1} - frac{3}{2} cdot 9x^{frac{3}{2} - 1} + frac{1}{2} cdot 2x^{frac{1}{2} - 1} + frac{1}{2} cdot x^{-frac{1}{2} - 1})Step: 3 ：Simplify to find the derivative: (f&#x27;(x) = 10x^2 - frac{27}{2}x + sqrt{x} - frac{1}{2sqrt{x}})

Find the derivative of the function \(f(x) = \frac{4x^3 - 9x^2 + 2x - 1}{\sqrt{x}}\)

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