Нет,не так.
180:15=12 штук штампцет за минуту
12*10=120штук он штампует за 10 минут
16, 36, 56, 76, 96
16/2 = 8
36/2 = (20+16)/2 = 18
56/2 = (40+16)/2 = 28
76/2 = (60+16)/2 = 38
96/2 = (80+16)/2 = 48
1. 18:6=3 литра-в 1 банке.
2.3*27=81литр
Ответ:81 литр налили в 27 банок
![y=\dfrac{x^2e^2}{x^2+3}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7Bx%5E2e%5E2%7D%7Bx%5E2%2B3%7D)
Найти производную можно парой способов:
1) По-честному:
Использовать формулу производной частного двух функций, т.е. если
, то ![f'(x)=\dfrac{g'(x)\cdot h(x)-h'(x)\cdot g(x)}{h^2(x)}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cdfrac%7Bg%27%28x%29%5Ccdot+h%28x%29-h%27%28x%29%5Ccdot+g%28x%29%7D%7Bh%5E2%28x%29%7D)
![\medskip \\ y'=e^2\left(\dfrac{x^2}{x^2+3}\right)'=e^2\left(\dfrac{(x^2)'(x^2+3)-x^2(x^2+3)'}{(x^2+3)^2}\right)=\medskip\\=e^2\left(\dfrac{2x(x^2+3)-2x^3}{(x^2+3)^2}\right)=e^2\left(\dfrac{2x^3+6x-2x^3}{(x^2+3)^2}\right)=\dfrac{e^{2}6x}{(x^2+3)^2}](https://tex.z-dn.net/?f=%5Cmedskip+%5C%5C+y%27%3De%5E2%5Cleft%28%5Cdfrac%7Bx%5E2%7D%7Bx%5E2%2B3%7D%5Cright%29%27%3De%5E2%5Cleft%28%5Cdfrac%7B%28x%5E2%29%27%28x%5E2%2B3%29-x%5E2%28x%5E2%2B3%29%27%7D%7B%28x%5E2%2B3%29%5E2%7D%5Cright%29%3D%5Cmedskip%5C%5C%3De%5E2%5Cleft%28%5Cdfrac%7B2x%28x%5E2%2B3%29-2x%5E3%7D%7B%28x%5E2%2B3%29%5E2%7D%5Cright%29%3De%5E2%5Cleft%28%5Cdfrac%7B2x%5E3%2B6x-2x%5E3%7D%7B%28x%5E2%2B3%29%5E2%7D%5Cright%29%3D%5Cdfrac%7Be%5E%7B2%7D6x%7D%7B%28x%5E2%2B3%29%5E2%7D)
2) Немного схитрим:
Можно просто поделить столбиком, но воспользуемся заменой переменной
![e^2\left(\dfrac{x^2}{x^2+3}\right) \medskip \\ x^2+3=\varphi \Rightarrow x^2=\varphi-3 \medskip \\ e^2\left(\dfrac{\varphi -3}{\varphi}\right)=e^2\left(1-\dfrac{3}{\varphi}\right) \medskip \\ y=e^2\left(1-\dfrac{3}{x^2+3}\right) \medskip \\ y'=e^2\left[0-\left(\dfrac{3}{x^2+3}\right)'\right]=-e^2\cdot\left[3\left((x^2+3)^{-1}\right)'\right]=\medskip\\=-3e^2\cdot(-1)(x^2+3)^{-2}\cdot 2x=6xe^2(x^2+3)^{-2}=\dfrac{6xe^2}{(x^2+3)^2}](https://tex.z-dn.net/?f=e%5E2%5Cleft%28%5Cdfrac%7Bx%5E2%7D%7Bx%5E2%2B3%7D%5Cright%29%0A%5Cmedskip%0A%5C%5C%0Ax%5E2%2B3%3D%5Cvarphi+%5CRightarrow+x%5E2%3D%5Cvarphi-3%0A%5Cmedskip%0A%5C%5C%0Ae%5E2%5Cleft%28%5Cdfrac%7B%5Cvarphi+-3%7D%7B%5Cvarphi%7D%5Cright%29%3De%5E2%5Cleft%281-%5Cdfrac%7B3%7D%7B%5Cvarphi%7D%5Cright%29%0A%5Cmedskip%0A%5C%5C%0Ay%3De%5E2%5Cleft%281-%5Cdfrac%7B3%7D%7Bx%5E2%2B3%7D%5Cright%29%0A%5Cmedskip%0A%5C%5C%0Ay%27%3De%5E2%5Cleft%5B0-%5Cleft%28%5Cdfrac%7B3%7D%7Bx%5E2%2B3%7D%5Cright%29%27%5Cright%5D%3D-e%5E2%5Ccdot%5Cleft%5B3%5Cleft%28%28x%5E2%2B3%29%5E%7B-1%7D%5Cright%29%27%5Cright%5D%3D%5Cmedskip%5C%5C%3D-3e%5E2%5Ccdot%28-1%29%28x%5E2%2B3%29%5E%7B-2%7D%5Ccdot+2x%3D6xe%5E2%28x%5E2%2B3%29%5E%7B-2%7D%3D%5Cdfrac%7B6xe%5E2%7D%7B%28x%5E2%2B3%29%5E2%7D)
Как видим результаты получились одинаковые