Verified answer

1) z_x = 3 ( x^4 + x - y)² { 4 x^3 + 1 } ---> z_xy = 6 ( x^4 + x - y) ( -1) { 4x^3 + 1 }

3) z_x = { 3x² } [ e^√(4xy) ] + x^3 { e^√(4xy) [ 2y / √ ( 4xy) ] }

difficult ? these are just products and quotients

For convenience, i will teach 'del' (partial) as 'd' (meaning d and del might want to both by utilising denoted with d). note that there is a distinction, even if that, yet I have deemed it beside the point for this calculation. in the starting up, the formula: dw/dr = dw/dx*dx/dr + dw/dy*dy/dr + dw/dz*dz/dr dw/ds = dw/dx*dx/ds + dw/dy*dy/ds + dw/dz*dz/ds dw/dt = dw/dx*dx/dt + dw/dy*dy/dt + dw/dz*dz/dt And calculate the derivatives: dw/dx = -7y + 7 dw/dy = -7x + 10 dw/dz = 0 dx/dr = a million dx/ds = a million dx/dt = a million dy/dr = a million dy/ds = a million dy/dt = 0 dz/dr = 0 dz/ds = a million dz/dt = a million Plug those in: dw/dr = (-7y+7)*a million + (-7x+10)*a million + 0 = -7x-7y+17 dw/ds = (-7y+7)*a million + (-7x+10)*a million + 0 = -7x-7y+17 dw/dt = (-7y+7)*a million + 0 + 0 = -7y+7 teach in words of r, s, and t: -7x-7y+17 = - 7( r+s+t ) - 7(r+s) + 17 -7x-7y+17 = - 7( r+s+t ) - 7(r+s) + 17 -7y+7 = -7( r+s ) +7 Plug on your element: dw/dr = -7(3)-7(5)+17 = -39 dw/ds = -7(3)-7(5)+17 = -39 dw/dt = -7(5)+7 = -28 and view your solutions! i wish this facilitates!