Question

Z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s , ∂z ∂t , ∂z ∂u when s = 1, t = 4, u = 5

Answer 1

$x(1,4,5)=4$
$y(1,4,5)=100$

$z_s=z_xx_s+z_yy_s=(4x^3+2xy)(1)+x^2(tu^2)$
$z_s(1,4,5)=1,024,000$

$z_t=z_xx_t+z_yy_t=(4x^3+2xy)(2)+x^2(su^2)$
$z_t(1,4,5)=1,331,200$

$z_u=z_xx_u+z_yy_u=(4x^3+2xy)(-1)+x^2(2st)$
$z_u(1,4,5)=-450,560$