Need help with logarithmic differentitation I have the expression
$$y = \sqrt{x^2(x+1)(x+2)}.$$
I have tried looking at videos but I still cannot arrive at the correct answer and don't know how to get there.
By the way, the correct answer is
$$y' = \frac{4x^2+9x+4}{2\sqrt{(x+1)(x+2)}}.$$
Please, help.

$$y = \sqrt{x^2 (x+1)(x+2)}$$
$$\ln{y} = \ln{x} + \frac12 \ln{(x+1)} + \frac12 \ln{(x+2)}$$
$$\frac{y'}{y} = \frac{1}{x} + \frac12 \frac{1}{x+1} + \frac12 \frac{1}{x+2}$$
$$y' = x \sqrt{(x+1)(x+2)} \left (  \frac{1}{x} + \frac12 \frac{1}{x+1} + \frac12 \frac{1}{x+2}\right) = x \sqrt{(x+1) (x+2)} \left ( \frac{4 x^2+9 x+4}{2 x(x+1)(x+2)}\right)$$
which I believe works out to your answer.
