Question

$\frac{d}{dt}(\frac{at+b}{x})=?$

Answer 1

\frac{a}{x}

Answer 2

The derivative is taken with respect to $t$. The expression is $\frac{at+b}{x}$. Assume $a, b,$ and $x$ are constants with respect to $t$.

$\frac{d}{dt}\left(\frac{at+b}{x}\right) = \frac{1}{x} \frac{d}{dt}(at+b)$

$\frac{d}{dt}(at+b) = \frac{d}{dt}(at) + \frac{d}{dt}(b) = a \cdot 1 + 0 = a$

So, $\frac{d}{dt}\left(\frac{at+b}{x}\right) = \frac{1}{x} \cdot a = \frac{a}{x}$.