Here is the problem as well as my work so far. Any advice or hints regarding where I should go from here would be appreciated.The arrow indicates where I got stuck.
Where do I go from here?
EDIT
I realize my mistake in not using logarithms. Here is my second attempt. What should I try from here?
Best Answer
here is a way to do check your i will do it little differently. i will start with $$\ln y = 5 \ln (x^2 + 3) - \frac 12 \ln (x+1) $$ differencing this we get $$\frac{dy}{y} = 5 \frac{d(x^2 + 3)}{x^2 + 3} - \frac{d(x+1)}{2(x+1)}=\frac{10x\, dx}{x^2 + 3} - \frac{dx}{2(x+1)} $$ therefore $$\frac{dy}{dx} = y\left(\frac{10x}{x^2 + 3} - \frac{1}{2(x+1)}\right)= \frac{(x^2+3)^3}{\sqrt{x+1}}\left(\frac{10x}{x^2 + 3} - \frac{1}{2(x+1)}\right)=\frac{(x^2+3)^2(19x^2+20x - 3)}{2(x+1)^{3/2}}$$