Find the derivative of the function.
\[
h(x)=\frac{4}{x^{2}}+\frac{4}{x^{3}}
\]
\[
h^{\prime}(x)=
\]
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Answer

\(\boxed{h^{\prime}(x)=-\frac{8}{x^{3}}-\frac{12}{x^{4}}}\) is the final answer.

Steps

Step 1 ：Rewrite the function \(h(x)=\frac{4}{x^{2}}+\frac{4}{x^{3}}\) as \(h(x)=4x^{-2}+4x^{-3}\).

Step 2 ：Apply the power rule for differentiation, which states that the derivative of \(x^n\) with respect to x is \(n*x^{n-1}\), to each term.

Step 3 ：This gives us \(h^{\prime}(x)=-8x^{-3}-12x^{-4}\).

Step 4 ：Rewrite \(h^{\prime}(x)=-8x^{-3}-12x^{-4}\) as \(h^{\prime}(x)=-\frac{8}{x^{3}}-\frac{12}{x^{4}}\).

Step 5 ：\(\boxed{h^{\prime}(x)=-\frac{8}{x^{3}}-\frac{12}{x^{4}}}\) is the final answer.