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Find the differential, \(\displaystyle dy\), of \(\displaystyle y = \sqrt{3 x^{3} - 5}\).

The differential is given by \(\displaystyle dy = f'(x)dx\). Using the formula gives:\begin{equation*} dy = \frac{9 x^{2}}{2 \sqrt{3 x^{3} - 5}}\,dx \end{equation*}

Download \(\LaTeX\)

\begin{question}Find the differential, $dy$, of $y = \sqrt{3 x^{3} - 5}$. 
    \soln{9cm}{The differential is given by $dy = f'(x)dx$. Using the formula gives:\begin{equation*} dy = \frac{9 x^{2}}{2 \sqrt{3 x^{3} - 5}}\,dx \end{equation*}}

\end{question}

Download Question and Solution Environment\(\LaTeX\)

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\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}

Find the differential, <img class="equation_image" title=" \displaystyle dy " src="/equation_images/%20%5Cdisplaystyle%20dy%20" alt="LaTeX: \displaystyle dy " data-equation-content=" \displaystyle dy " /> , of <img class="equation_image" title=" \displaystyle y = \sqrt{3 x^{3} - 5} " src="/equation_images/%20%5Cdisplaystyle%20y%20%3D%20%5Csqrt%7B3%20x%5E%7B3%7D%20-%205%7D%20" alt="LaTeX: \displaystyle y = \sqrt{3 x^{3} - 5} " data-equation-content=" \displaystyle y = \sqrt{3 x^{3} - 5} " /> .

The differential is given by <img class="equation_image" title=" \displaystyle dy = f'(x)dx " src="/equation_images/%20%5Cdisplaystyle%20dy%20%3D%20f%27%28x%29dx%20" alt="LaTeX: \displaystyle dy = f'(x)dx " data-equation-content=" \displaystyle dy = f'(x)dx " /> . Using the formula gives: <img class="equation_image" title=" dy = \frac{9 x^{2}}{2 \sqrt{3 x^{3} - 5}}\,dx " src="/equation_images/%20%20dy%20%3D%20%5Cfrac%7B9%20x%5E%7B2%7D%7D%7B2%20%5Csqrt%7B3%20x%5E%7B3%7D%20-%205%7D%7D%5C%2Cdx%20%20" alt="LaTeX: dy = \frac{9 x^{2}}{2 \sqrt{3 x^{3} - 5}}\,dx " data-equation-content=" dy = \frac{9 x^{2}}{2 \sqrt{3 x^{3} - 5}}\,dx " />