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Questions: Algebra BusinessCalculus
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Find the anti-derivative of \(\displaystyle f(x) = \frac{1}{x^{\frac{4}{5}}}\).
Writing the function with a negative rational (fractional) exponent and using the power rule gives \begin{equation*}F(x) = 5 \sqrt[5]{x} + C\end{equation*}
\begin{question}Find the anti-derivative of $f(x) = \frac{1}{x^{\frac{4}{5}}}$.
\soln{4cm}{Writing the function with a negative rational (fractional) exponent and using the power rule gives
\begin{equation*}F(x) = 5 \sqrt[5]{x} + C\end{equation*}}
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Find the anti-derivative of <img class="equation_image" title=" \displaystyle f(x) = \frac{1}{x^{\frac{4}{5}}} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cfrac%7B1%7D%7Bx%5E%7B%5Cfrac%7B4%7D%7B5%7D%7D%7D%20" alt="LaTeX: \displaystyle f(x) = \frac{1}{x^{\frac{4}{5}}} " data-equation-content=" \displaystyle f(x) = \frac{1}{x^{\frac{4}{5}}} " /> . </p> </p><p> <p>Writing the function with a negative rational (fractional) exponent and using the power rule gives
<img class="equation_image" title=" F(x) = 5 \sqrt[5]{x} + C " src="/equation_images/%20F%28x%29%20%3D%205%20%5Csqrt%5B5%5D%7Bx%7D%20%2B%20C%20" alt="LaTeX: F(x) = 5 \sqrt[5]{x} + C " data-equation-content=" F(x) = 5 \sqrt[5]{x} + C " /> </p> </p>