I am given the following partial differential of a Gaussian where the variance is a function of $t$, $\Xi(t)$ as follows:
$$\frac{\partial}{\partial t} \frac{1}{\sqrt{2\pi \Xi(t)}}\cdot\exp\bigg[\frac{-z^2}{2 \Xi(t)} \bigg]$$
Apparently this can be rewritten as:
$$=\bigg[- \frac{1}{2 \Xi(t)} + \frac{z^2}{2 \Xi(t)^2} \bigg]\bigg(\frac{d \Xi}{dt}\bigg) \frac{1}{\sqrt{2\pi \Xi(t)}}\cdot\exp\bigg[\frac{-z^2}{2 \Xi(t)} \bigg]$$
I can see that the term in front looks it stems from differentiating the exponential but I am not entirely sure how, and I do not get how the $\frac{d \Xi}{dt}$ term appears.
Any help is highly appreciated :-)