Chapter 13 - Partial Derivatives - 13.3 Partial Derivatives - Exercises Set 13.3 - Page 936: 4

$f_x(x,y)=20xy^4-6y^2+20x$ $f_y(x,y)=40x^2y^3-12xy$

Take the first partial derivatives of the given function. When taking partial derivative with respect to x, treat y as a constant, and vice versa: $f_x(x,y)=2*10x^1y^4-6*1y^2+2*10x^1=20xy^4-6y^2+20x$ $f_y(x,y)=4*10x^2y^3-2*6xy^2+0=40x^2y^3-12xy$