<s>[INST] Should the vertical "at bar" go before or after the function being differentiated? Suppose I want to calculate the derivative of a long function at a particular point $a$. Is it more common to write
$$
\frac{d}{dx} \left( x^2 \sin(x)^{(3x-1)^2} + \frac{e^x}{2 x^3 -2 x^2 +1} -3 \log(x)\right) \Bigg|_{x=a}
$$
or
$$
\frac{d}{dx}\Bigg|_{x=a} \left( x^2 \sin(x)^{(3x-1)^2} + \frac{e^x}{2 x^3 -2 x^2 +1} -3 \log(x) \right)?
$$
Does either notational convention have any advantages for clarity?
 [/INST] I agree with MathGeek.  Use the first one
$$
\frac{d}{dx} \left( x^2 \sin(x)^{(3x-1)^2} + \frac{e^x}{2 x^3 -2 x^2 +1} -3 \log(x)\right) \Bigg|_{x=a}
$$
(in mathematics).
However, I do not speak for engineering or physics.  The second notation
$$
\frac{d}{dx}\Bigg|_{x=a} \left( x^2 \sin(x)^{(3x-1)^2} + \frac{e^x}{2 x^3 -2 x^2 +1} -3 \log(x) \right)
$$
treats $\frac{d}{dx}\big|_{x=a}$ as an operator, and applies it to a function.
This is analogous to the notation for integrals (preferred in some parts of engineering and physics)
$$
\int_a^b\,dx\;\left( x^2 \sin(x)^{(3x-1)^2} + \frac{e^x}{2 x^3 -2 x^2 +1} -3 \log(x) \right)
$$
whereas in mathematics we prefer
$$
\int_a^b\;\left( x^2 \sin(x)^{(3x-1)^2} + \frac{e^x}{2 x^3 -2 x^2 +1} -3 \log(x) \right)\,dx
$$
</s>