Question

If $y=\log \left[e^{3x}{\left(\frac{x-4}{x+3}\right)}^{\frac{2}{3}}\right]$, find $\frac{dy}{dx}$

Answer 1

$y\log \left[e^{3x}{\left(\frac{x-4}{x+3}\right)}^{2/3}\right]$

$\Rightarrow y=\log e^{3x}+\frac{2}{3}\log \left(\frac{x-4}{x+3}\right)$

$\Rightarrow y=3x+\frac{2}{3}\log (x-4)-\frac{2}{3}\log (x+3)$

$\therefore \frac{dy}{dx}=3+\frac{2}{3(x-4)}-\frac{2}{3(x+4)}$ Ans.