1) Let's Differentiate the function below applying the Power Rule.
2) Let's rewrite those radicals as powers firstly
[tex]\begin{gathered} f(x)=9x^3-6\sqrt[]{x}+\frac{3}{x^3}-\frac{5}{\sqrt[4]{x}} \\ f(x)\text{ = }9x^3-6x^{\frac{1}{2}}+3x^{-3\text{ }}-5x^{\frac{-1}{4}} \end{gathered}[/tex]
3) Let's apply the Power Rule now, subtracting one unit from the exponent and multiplying the base by the original exponent
[tex]f^{\prime}(x)=27x^2-3x^{-\frac{1}{2\text{ }}}-9x^{-4}+\frac{5}{4}x^{-\frac{5}{4}}[/tex]
