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Уважаемые эксперты, очень вас прошу помогите решить следующие задания: Найти производную dy/dx данных функций. 1) y=cosln^2x (косинус (лн в квадрате) икс не в квадрате) 2) y=(e (в степени sin x) -1) и все это в квадрате 3) y=2x в степени корень из x 4) y=(1 делить на ( корень третьей степени, под корнем 2x-1)) ко всему этому прибавлям ( 5 делить на ( корень четвертой степени, под корнем в скобках x в кубе +2, и эта скобка в кубе)
Найти dy/dx и (d в квадрате y / dx в квадрате 1) y= корень третьей степени, под корнем в скобках (1-х) в квадрате 2) x= arcsin(t в квадрате -1) y= arccos2t
В прямоугольной системе координат через точку (1,4) проведена прямая, пересекающаяся с положительными полуосями координат. Написать уравнение прямой, если сумма отрезков, отсекаемых ею на осях координат, принимает наименьшее значение.
Найти работу, необходимую для того, чтобы выкачать воду из полусферического сосуда, диаметр которого равен 20 м.
x/a + y/b=1 - уравнение прямой в отрезках на осях Точка (1, 4) принадлежит прямой, значит ее координаты удовлетворяют уравнение прямой 1/а + 4/b=1 4/b=1-1/a=(a-1)/a b=4a/(a-1) Сумма отрезков, отсекаемых на осях S=a+b=a+ 4a/(a-1)=(a*(a-1)+4a)/(a-1) должна быть наименьшей, значит S'=0 S'=((a2+3a)(a-1))'=[(2a+3)*(a-1)-(a2+3a)]/(a-1)2=(2a2+a-3-a2-3a)/(a-1)2= =(a2-2a-3)/(a-1)2=0 a2-2a-3=0 D=4+12=16 a1=(2+4)/2=3 a2=(2-4)/2=-1 Поскольку а - длина отрезка, то a>0, значит а=3 Тогда b=4a/(a-1) b=12/2=6 Уравнение прямой x/3 + y/6=1
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