If y = log left[a^{3x} left(frac{5-x}{x+4}rig | vedclass

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(D) Given $y = \log \left[a^{3x} \left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right]$.Using the properties of logarithms,$\log(mn) = \log m + \log n$ an

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$3 \log a - \frac{3}{4(5-x)} - \frac{3}{4(x+4)}$

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(D) Given $y = \log \left[a^{3x} \left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right]$.Using the properties of logarithms,$\log(mn) = \log m + \log n$ and $\log(m^n) = n \log m$:$y = \log(a^{3x}) + \log\left(\left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right)$$y = 3x \log a + \frac{3}{4} \log(5-x) - \frac{3}{4} \log(x+4)$Differentiating with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}(3x \log a) + \frac{3}{4} \frac{d}{dx}(\log(5-x)) - \frac{3}{4} \frac{d}{dx}(\log(x+4))$$\frac{dy}{dx} = 3 \log a + \frac{3}{4} \left(\frac{1}{5-x}\right)(-1) - \frac{3}{4} \left(\frac{1}{x+4}\right)(1)$$\frac{dy}{dx} = 3 \log a - \frac{3}{4(5-x)} - \frac{3}{4(x+4)}$

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

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