If $w=f(x,y,z)=5x^{2}yz^{3}$, then $$f_{x}(x,y,z)=10xyz^{3}\qquad f_{y}(x,y,z)=5x^{2}z^{3}\qquad f_{z}(x,y,z)=15x^{2}yz^{2}$$