Scipy minimize using analytical gradients

[ProxyCausal]

I'm wondering why in the budget optimizer analytical gradients are not used instead of finite difference since they are faster and more accurate. With large dataset finite difference doesn't seem feasible. It seems gradients for adstock and hill isn't hard to calculate in analytical form.

[juanitorduz]

@ProxyCausal would you like to try opening a PR? :)

[wd60622]

Should be able to make use of pytensor for the derivatives. pt.grad is the function?