А) 4 дм2=(4*100)см2 = 400см2
<span>б) 6 м2=(6*100)дм2 = 600дм2 </span>
Ответ:
![\frac{\partial f}{\partial l}=-8\sqrt{3}+10](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+l%7D%3D-8%5Csqrt%7B3%7D%2B10)
Пошаговое объяснение:
![\frac{\partial f}{\partial l}=\frac{\partial f }{\partial x}\cos(\alpha)+\frac{\partial f}{\partial y}\cos(\beta)](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+l%7D%3D%5Cfrac%7B%5Cpartial+f+%7D%7B%5Cpartial+x%7D%5Ccos%28%5Calpha%29%2B%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+y%7D%5Ccos%28%5Cbeta%29)
Найдем угол бета:
![\beta=90\textdegree-\alpha=90\textdegree-30\textdegree=60\textdegree](https://tex.z-dn.net/?f=%5Cbeta%3D90%5Ctextdegree-%5Calpha%3D90%5Ctextdegree-30%5Ctextdegree%3D60%5Ctextdegree)
Теперь найдем косинусы этих углов:
![\cos(\alpha)=\frac{\sqrt{3}}{2}\\\cos(\beta)=\frac{1}{2}](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5C%5C%5Ccos%28%5Cbeta%29%3D%5Cfrac%7B1%7D%7B2%7D)
Осталось найти частные производные и их значение в точке А:
![\frac{\partial f}{\partial x}=-8xy-4y^3\\\frac{\partial f}{\partial x}(A)=-8*(-1)*2-4*2^3=-16\\\frac{\partial f}{\partial y}=-12y-4x^2-12xy^2\\\frac{\partial f}{\partial x}(A)=-12*2-4*(-1)^2-12*(-1)*2^2=20](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+x%7D%3D-8xy-4y%5E3%5C%5C%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+x%7D%28A%29%3D-8%2A%28-1%29%2A2-4%2A2%5E3%3D-16%5C%5C%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+y%7D%3D-12y-4x%5E2-12xy%5E2%5C%5C%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+x%7D%28A%29%3D-12%2A2-4%2A%28-1%29%5E2-12%2A%28-1%29%2A2%5E2%3D20)
Находим производную:
![\frac{\partial f}{\partial l}=-16*\frac{\sqrt{3}}{2}+20*\frac{1}{2}=-8\sqrt{3}+10](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+l%7D%3D-16%2A%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2B20%2A%5Cfrac%7B1%7D%7B2%7D%3D-8%5Csqrt%7B3%7D%2B10)
43/6равно 7 1/6, 23/9 равно 2 5/9