Question

how to solve this please elaborate

Answer 1

we have to find the derivative of the function ,$f(x)=log_e(2x)$ w.r.t t

$f(x)=log_e(2x)\\\\\text{differentiate with respect to t}\\\\\frac{df(x)}{dt}=\frac{d\{log_e(2x)\}}{dx}\\\\=\frac{1}{2x}\frac{d(2x)}{dx}\\\\=\frac{1}{2x}2\frac{dx}{dt}\\\\=\frac{1}{x}\frac{dx}{dt}$

hence, option (2) is correct.