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