If $y=\log \left[\mathrm{e}^{5 x}\left(\frac{3 x-4}{x+5}\right)^{\frac{4}{3}}\right]$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

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Aicharya · Accepted Answer

$\begin{aligned} y & =\log \left[\mathrm{e}^{5 x}\left(\frac{3 x-4}{x+5}ight)^{\frac{4}{3}}ight] \ 	herefore \quad y & =5 x \log \mathrm{e}+\frac{4}{3} \log (3 x-4)-\frac{4}{3} \log (x+5) \ 	herefore \quad \frac{\mathrm{d} y}{\mathrm{~d} x} & =5+\frac{4}{3(3 x-4)} 	imes 3-\frac{4}{3(x+5)} 	imes 1 \ & =5+\frac{4}{(3 x-4)}-\frac{4}{3(x+5)}\end{aligned}$

If $y=\log \left[\mathrm{e}^{5 x}\left(\frac{3 x-4}{x+5}\right)^{\frac{4}{3}}\right]$, then…

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