Are you confused about transformation of the "last line of your work" to the "given answer"?Please refer to the attachment - I am not sure how to get the answer that it is supposed to be...
Thank you!
problem statement says the function is
[MATH]y = \frac{\ln(x-5)}{2x+1} [/MATH]
you worked the derivative of
[MATH]y=\frac{\ln(x+5)}{2x+1}[/MATH]
,,,
[MATH]y’= \frac{(2x+1) \cdot \frac{1}{x-5} - 2 \cdot \ln(x-5)}{(2x+1)^2}[/MATH]
now, multiply numerator and denominator by [MATH](x-5)[/MATH] to clear the complex fraction in the numerator ... then split the resulting fraction
[MATH]\frac{(2x+1) \cdot \frac{1}{x-5} - 2\ln(x-5)}{(2x+1)^2} \cdot \frac{x-5}{x-5}[/MATH]
[MATH]\frac{(2x+1) - 2(x-5)\ln(x-5)}{(2x+1)^2(x-5)}[/MATH]
[MATH]\frac{2x+1}{(2x+1)^2(x-5)} - \frac{2(x-5) \ln(x-5)}{(2x+1)^2(x-5)}[/MATH]
finish it ...