What is the difference between a derivative and a total derivative? Please, help.

When you take a partial derivative, you operate under a sort of assumption that you hold one variable fixed while the other changes, while when computing a total derivative, you allow changes in one variable to affect the other.

So, for instance, if you have f(x,y)=2x+3y, then when you compute the partial derivative ${\displaystyle \frac{\partial f}{\partial x}}$, you temporarily assume y constant and treat it as such, yielding ${\displaystyle \frac{\partial f}{\partial x}=2+\frac{\partial \left(3y\right)}{\partial x}=2+0=2}$.
However, if ${\displaystyle x=x(r,\theta )}$ and ${\displaystyle y=y(r,\theta )}$, then the assumption that y stays constant when x changes is no longer valid. Since ${\displaystyle x=x(r,\theta )}$, then if x changes, it implies that at least one of r or${\displaystyle \theta }$ changes. And if r or ${\displaystyle \theta }$ change, then y changes. Thus, obviously it has some sort of effect on the derivative and we can no longer assume it to be equal to zero.