If $\displaystyle y, z, r$ are constants, then $\displaystyle \ln{(yzr)}$ is also a constant.
So $\displaystyle \frac{d}{dx}\left[-(x + 1)\ln{(yzr)}\right] = -x\ln{(yzr)}$.
Typo- that 'x' should not be in the final answer. This is simply -x C+ C (where I have written the constant ln(yzr) as "C"), linear in x, so its derivative is the constant -C= -ln(xzr).
Typo- that 'x' should not be in the final answer. This is simply -x C+ C (where I have written the constant ln(yzr) as "C"), linear in x, so its derivative is the constant -C= -ln(xzr).