In the following second-order partial differential equation for $f$ with $x$ and $t$ as independent variables, $a$ and $b$ as constants, and $g$ as a known function with $t$ as the only independent variable
$$a \frac{ \partial^2 f}{ \partial x^2 } + b \frac{ \partial f }{ \partial t } + \frac{ dg }{ dt } = 0$$
is the mathematically correct notation for the third term on the left-hand side $\frac{ dg }{ dt }$ as above, or $\frac{ \partial g }{ \partial t }$? Some may say that $\frac{ \partial g }{ \partial t }$ is correct because it is a term in a partial differential equation, but since $g$ is a one variable function with $t$ only, I think $\frac{ dg }{ dt }$ is correct according to the original usage of the derivative and partial derivative symbol. The original usage of the partial derivative symbol is to express the rate of change of a multivariable function of two or more variables when all variables except the variable to be used in the differentiation are fixed, and the notation $\frac{ \partial g }{ \partial t }$ implies that $g$ is not a one variable function, which would be somewhat inaccurate.