<span>Найдите производную функции
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![y=e^{4x+5}](https://tex.z-dn.net/?f=y%3De%5E%7B4x%2B5%7D)
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Решение
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![y'=(e^{4x+5})' =e^{4x+5}*(4x+5)'=e^{4x+5}*((4x)'+(5)')=](https://tex.z-dn.net/?f=y%27%3D%28e%5E%7B4x%2B5%7D%29%27+%3De%5E%7B4x%2B5%7D%2A%284x%2B5%29%27%3De%5E%7B4x%2B5%7D%2A%28%284x%29%27%2B%285%29%27%29%3D)
![e^{4x+5}*(4+0)=4e^{4x+5}](https://tex.z-dn.net/?f=e%5E%7B4x%2B5%7D%2A%284%2B0%29%3D4e%5E%7B4x%2B5%7D)
Если функция записана как
![y=e^{4x}+5](https://tex.z-dn.net/?f=y%3De%5E%7B4x%7D%2B5)
![y'=(e^{4x}+5)' =e^{4x}*(4x)'+(5)'=4e^{4x}](https://tex.z-dn.net/?f=y%27%3D%28e%5E%7B4x%7D%2B5%29%27+%3De%5E%7B4x%7D%2A%284x%29%27%2B%285%29%27%3D4e%5E%7B4x%7D)
Найдем стоимость 500 кг чая по 35 рублей
500*35=17500
Пусть х кг чая по 30 рублей за 1 кг
у кг чая по цене 50 рублей за 1 кг
тогда по условию
х+у=500
30х+50у=17500
или
х+у=500 3х+3у=1500
3х+5у=1750 3х+5у=1750
2у=250
у=125
500-125=375
Итак, .........................................................
Y = x^2 - 4x
y = 0
x^2 - 4x = 0
x * (x - 4) = 0
x = 0; x = 4
Ответ: (0,0), (4,0)