-z*(z - 1)*(y*(c5 - r5)*(x - 1) - w4*x*(y - 1) + x*(c6 - r6)*(y - 1) + w4*(x - 1)*(y - 1) - (c7 - r7)*(x - 1)*(y - 1) + w4*x*y - x*y*(c5 - r5))对z求一阶导,并对结果化简
时间: 2023-10-21 18:03:53 浏览: 120
对 $z$ 求一阶导数,可以将其他变量视为常数,得到:
$- (z - 1) * (y*(c5 - r5)*(x - 1) - w4*x*(y - 1) + x*(c6 - r6)*(y - 1) + w4*(x - 1)*(y - 1) - (c7 - r7)*(x - 1)*(y - 1) + w4*x*y - x*y*(c5 - r5)) - z*(y*(c5 - r5)*(x - 1) - w4*x*(y - 1) + x*(c6 - r6)*(y - 1) + w4*(x - 1)*(y - 1) - (c7 - r7)*(x - 1)*(y - 1) + w4*x*y - x*y*(c5 - r5))'$
对右边的函数进行求导,可以得到:
$- (y*(c5 - r5)*(x - 1) - w4*x*(y - 1) + x*(c6 - r6)*(y - 1) + w4*(x - 1)*(y - 1) - (c7 - r7)*(x - 1)*(y - 1) + w4*x*y - x*y*(c5 - r5)) - z*(-(y*(c5 - r5)) + x*(c6 - r6) + w4*(y - 1) - (c7 - r7)*(y - 1) + w4*x - x*y*(c5 - r5))$
化简后,可得:
$w4*x - c6*x*y + r6*x*y + (c7-r7)*x*z*y - w4*z + w4*y - c5*x*y*z + r5*x*y*z + (c7-r7)*x*z - w4*(y-1) + (c7-r7)*(y-1) + y*(c5-r5)*z - y*(c5-r5) - x*(c6-r6)*z + x*(c6-r6) + (c7-r7)*(x-1)*y - (c7-r7)*(x-1)$
因此,一阶导数为:
$(c5*y - c6*x*y + r5*x*y - r6*x*y + (c7-r7)*x*y - c5*x*y*z + r5*x*y*z + (c7-r7)*x*z - c7*x + r7*x + w4*y + (c7-r7)*(y-1) - w4*x - w4*(y-1) + y*(c5*z - c5 - 1) - x*(c6*z - c6) - z*w4)$
化简后的结果为:
$(c5*(y*z - y - z + 1) - c6*x*y*(z-1) + r5*x*y*(z-1) - r6*x*y*(z-1) + (c7-r7)*x*y*(1-z) + (c7-r7)*x*(z-1) - c7*x + r7*x + w4*y - w4*x*z + (c7-r7)*(y-1))$
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