Differential coefficient of $log_{10}x$ with respect to $log_{x}10$ is :

$-(x\, log_{10}x)^2$ $-\frac{(log_{10}x)^2}{x^2}$ $-\frac{1}{(log_{10}x10)^2}$ $-\frac{x}{(log_{10}x)^2}$

$-\frac{1}{(log_{10}x10)^2}$