Question

log_x² x

Answer 1

$$\begin{gathered} {\log }_{x^2}x=\frac{\log x}{\log x^2}\text{(by change of base property)} \\ =\frac{\log x}{2\log x}\left[\log x^2=2\log x\right] \\ =\frac{1}{2} \\ \text{Now}\frac{d}{dx}\left({\log }_{x^2}x\right)\mathrm{=}\frac{d}{dx}\left(\frac{1}{2}\right) \\ =0\left(\text{∵}\frac{1}{2}\text{is a constant}\right) \end{gathered}$$