Differentiation, logarithmic fucntion

Question

The Derivative of $\log_{10} x$ with respect to $x^2$ is?
The Answer is having loge(base10)

Answer 1

Let y= $\log_{10}x=\frac{\ln x}{\ln 10} $ via Change of base

and $t=x^2$

Now $$\frac{dy}{dt}=\frac{dy}{dx}\frac{dx}{dt}=\frac{1}{x \ln 10}*\frac{1}{2x}$$