Find the requested partial derivative dzdy if z3zxy1 and y3x

Solution

z^3=z+xy-1 differentiate wrt x 3z^2dz/dx = dz/dx + y (3z^2-1)dz/dx = y dz/dx = y/(3z^2-1) y^3=x+y-1 differentiate wrt x 3y^2dy/dx = 1 + dy/dx (3y^2-1)dy/dx = 1 dy/dx = 1/(3y^2-1) dz/dy = dz/dx * dx/dy dz/dy = y(3y^2-1)/(3z^2-1)