I'm reading math notes online here. In the notes there is a problem that differentiates the following equation:
$$ \sec(A) = \frac x {50};$$
...where the angle $A$ is a function of time (ie. $A = A(t)$)
The answer for which is:
$$ \sec(A)\tan(A) A' = \frac{x'}{50};$$
I understand the differentiation of the left side of the equation but I don't understand why the derivative of the right side equates to x' / 50...why isn't the right side differentiated like so:
$$\frac1{50} \frac{\mathrm d}{\mathrm dx}(x) = \frac1{50}\cdot1 = \frac1{50}$$
It seems that in the context in which the linked page is writing, an expression like $A'$ means $dA/dt$, not $dA/dx$, and $x'$ means $dx/dt$, not $dx/dx$. If it were $dx/dx$, then it would be $1$. So $$ \frac{d}{dt} \sec A = \sec A\tan A\cdot\frac{dA}{dt}\quad\text{and}\quad \frac{d}{dt} \frac x{50} = \frac{dx/dt}{50}. $$