-y*(y - 1)*(c3*x*(z - 1) - w3*z*(x - 1) + z*(c4 - r4)*(x - 1) - c4*(x - 1)*(z - 1) + w2*x*z - x*z*(c3 - r3))对y求一阶导
时间: 2023-10-21 20:59:10 浏览: 42
对 $y$ 求一阶导数,可以将其他变量视为常数,得到:
$- (y - 1) * (c3*x*(z - 1) - w3*z*(x - 1) + z*(c4 - r4)*(x - 1) - c4*(x - 1)*(z - 1) + w2*x*z - x*z*(c3 - r3)) - y*(c3*x*(z - 1) - w3*z*(x - 1) + z*(c4 - r4)*(x - 1) - c4*(x - 1)*(z - 1) + w2*x*z - x*z*(c3 - r3))'$
对右边的函数进行求导,可以得到:
$- (c3*x*(z - 1) - w3*z*(x - 1) + z*(c4 - r4)*(x - 1) - c4*(x - 1)*(z - 1) + w2*x*z - x*z*(c3 - r3)) - y*(-c3*(z-1) + z*(c4-r4) - c4*(x-1) - x*z*(c3-r3))$
化简后,可得:
$- c3*x*(z - 1) + w3*z*(x - 1) - z*(c4 - r4)*(x - 1) + c4*(x - 1)*(z - 1) - w2*x*z + x*z*(c3 - r3) + c3*y*(z - 1) - z*(c4 - r4)*y + c4*(x - 1)*y + x*z*(c3 - r3)*y$
因此,一阶导数为:
$c3*(y-1)*(z-1) - z*(c4-r4)*(y-1) - c4*(x-1)*(y-1) + x*z*(c3-r3)*(y-1) - c3*y*(z-1) + z*(c4-r4)*y - c4*(x-1)*y - x*z*(c3-r3)*y$