Chapter 13 - Partial Derivatives - 13.3 Partial Derivatives - Exercises Set 13.3 - Page 936: 9

$z_x=cos(5x^3y+7xy^2)(15x^2y+7y^2)$ $z_y=cos(5x^3y+7xy^2)(5x^3+14xy)$

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: $z_x=cos(5x^3y+7xy^2)*(3*5x^2y+7y^2)=cos(5x^3y+7xy^2)(15x^2y+7y^2)$ $z_y=cos(5x^3y+7xy^2)*(5x^3+2*7xy)=cos(5x^3y+7xy^2)(5x^3+14xy)$