Apologies if this is a dumb question. I learned at school that I can differentiate $y=x^{2}$ to give $\frac{dy}{dx}=2x.$ But, if I have a multivariable function, for example$y=4x^{2}+3z+t^{3}$ am I allowed to differentiate it to give$dy=8x\;dx+3\;dz+3t^{2}\;dt$ and, if valid, what is this procedure called exactly?
Thank you