-x*(x - 1)*(c1*y*(z - 1) + w1*z*(y - 1) + z*(c2 - r2)*(y - 1) - c2*(y - 1)*(z - 1) - w1*y*z - y*z*(c1 - r1))对x求一阶导
时间: 2023-10-21 22:59:10 浏览: 175
一阶导数的微分1
对于这个多项式函数,我们需要使用乘法法则和链式法则来求解一阶导数。首先,我们应用乘法法则将函数展开:
-x*(x - 1)*(c1*y*(z - 1) + w1*z*(y - 1) + z*(c2 - r2)*(y - 1) - c2*(y - 1)*(z - 1) - w1*y*z - y*z*(c1 - r1))
= -x*(x - 1)*(c1*y*z - c1*y - w1*y + c1*z - c1 - w1*z + c2*y*z - r2*y*z - c2*y + c2*z - c2 - y*z*c1 + y*z*r1)
然后,我们对该多项式函数求一阶导数,应用链式法则:
d/dx (-x*(x - 1)*(c1*y*z - c1*y - w1*y + c1*z - c1 - w1*z + c2*y*z - r2*y*z - c2*y + c2*z - c2 - y*z*c1 + y*z*r1))
= -((x - 1)*(c1*y*z - c1*y - w1*y + c1*z - c1 - w1*z + c2*y*z - r2*y*z - c2*y + c2*z - c2 - y*z*c1 + y*z*r1)) - x*(2*x - 1)*(c1*y*z - c1*y - w1*y + c1*z - c1 - w1*z + c2*y*z - r2*y*z - c2*y + c2*z - c2 - y*z*c1 + y*z*r1)
= -(x^2*(c1*y*z - c1*y - w1*y + c1*z - c1 - w1*z + c2*y*z - r2*y*z - c2*y + c2*z - c2 - y*z*c1 + y*z*r1) - x*(c1*y*z - c1*y - w1*y + c1*z - c1 - w1*z + c2*y*z - r2*y*z - c2*y + c2*z - c2 - y*z*c1 + y*z*r1))
= -(x^2*c1*y*z - x^2*c1*y - x^2*w1*y + x^2*c1*z - x^2*c1 - x^2*w1*z + x^2*c2*y*z - x^2*r2*y*z - x^2*c2*y + x^2*c2*z - x^2*c2 - x^2*y*z*c1 + x^2*y*z*r1 - x*c1*y*z + x*c1*y + x*w1*y - x*c1*z + x*c1 + x*w1*z - x*c2*y*z + x*r2*y*z + x*c2*y - x*c2*z + x*c2 + y*z*c1 - y*z*r1)
因此,该多项式函数对x的一阶导数为:
-(x^2*c1*y*z - x^2*c1*y - x^2*w1*y + x^2*c1*z - x^2*c1 - x^2*w1*z + x^2*c2*y*z - x^2*r2*y*z - x^2*c2*y + x^2*c2*z - x^2*c2 - x^2*y*z*c1 + x^2*y*z*r1 - x*c1*y*z + x*c1*y + x*w1*y - x*c1*z + x*c1 + x*w1*z - x*c2*y*z + x*r2*y*z + x*c2*y - x*c2*z + x*c2 + y*z*c1 - y*z*r1)
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