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

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Aicharya · Accepted Answer

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

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

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