Respuesta :

Given:

[tex]f(x)=x^2+3x^{-3}[/tex]

The first derivative is:

[tex]\begin{gathered} f^{\prime}(x)=2x^{2-1}+3\cdot(-3)x^{-3-1} \\ Simplify \\ f^{\prime}(x)=2x-9x^{-4} \end{gathered}[/tex]

And the second derivative is:

[tex]f^{\prime}^{\prime}(x)=2x^{1-1}-9(-4)x^{-4-1}=2(1)+36x^{-5}=2+36x^{-5}[/tex]

Answer:

[tex]\begin{equation*} 2+36x^{-5} \end{equation*}[/tex]

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