3 раза
3*10+20=50
Так или не так??
А)40÷100×25=10, б)800÷100×4= 32
9м =0,009км = 9/1000 км
1сек.= 1/60мин.= 1/3600 часа
9/1000 : 1/3600 = 9/1000 : 1/3600 = 162/5 = 32,4(км/ч
Типо так?
x^5=-1/32
x=корень 5 степени из (-1/32)
<span>x=-1/2</span>
<span>Найдите производные dy/dx данной функции
66)a)
![y=5 \sqrt[5]{x^3+1}+ \frac{1}{x}](https://tex.z-dn.net/?f=y%3D5+%5Csqrt%5B5%5D%7Bx%5E3%2B1%7D%2B+%5Cfrac%7B1%7D%7Bx%7D++)
b)
![y=tg^3(x^2+1)](https://tex.z-dn.net/?f=y%3Dtg%5E3%28x%5E2%2B1%29)
Решение
a)
![y'=(5\sqrt[5]{x^3+1}+ \frac{1}{x})'=(5(x^3+1)^{ \frac{1}{5} })'+ (x^{-1})'=](https://tex.z-dn.net/?f=y%27%3D%285%5Csqrt%5B5%5D%7Bx%5E3%2B1%7D%2B+%5Cfrac%7B1%7D%7Bx%7D%29%27%3D%285%28x%5E3%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B5%7D+%7D%29%27%2B+%28x%5E%7B-1%7D%29%27%3D)
![5* \frac{1}{5} (x^3+1)^{ \frac{1}{5}-1 }*(x^3+1)'- x^{-2}=(x^3+1)^{ -\frac{4}{5}}*3x^2- \frac{1}{x^2}=](https://tex.z-dn.net/?f=5%2A+%5Cfrac%7B1%7D%7B5%7D+%28x%5E3%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B5%7D-1+%7D%2A%28x%5E3%2B1%29%27-+x%5E%7B-2%7D%3D%28x%5E3%2B1%29%5E%7B+-%5Cfrac%7B4%7D%7B5%7D%7D%2A3x%5E2-++%5Cfrac%7B1%7D%7Bx%5E2%7D%3D)
![= \frac{3x^2}{ \sqrt[5]{(x^3+1)^4} }- \frac{1}{x^2}](https://tex.z-dn.net/?f=%3D+%5Cfrac%7B3x%5E2%7D%7B+%5Csqrt%5B5%5D%7B%28x%5E3%2B1%29%5E4%7D+%7D-++%5Cfrac%7B1%7D%7Bx%5E2%7D+)
b)
![y'=(tg^3(x^2+1))'=3tg^2(x^2+1)*(tg(x^2+1))'=](https://tex.z-dn.net/?f=y%27%3D%28tg%5E3%28x%5E2%2B1%29%29%27%3D3tg%5E2%28x%5E2%2B1%29%2A%28tg%28x%5E2%2B1%29%29%27%3D+)
![3tg^2(x^2+1)* \frac{1}{cos^2(x^2+1)}*(x^2+1)'=3tg^2(x^2+1)* \frac{1}{cos^2(x^2+1)}*2x=](https://tex.z-dn.net/?f=3tg%5E2%28x%5E2%2B1%29%2A+%5Cfrac%7B1%7D%7Bcos%5E2%28x%5E2%2B1%29%7D%2A%28x%5E2%2B1%29%27%3D3tg%5E2%28x%5E2%2B1%29%2A+%5Cfrac%7B1%7D%7Bcos%5E2%28x%5E2%2B1%29%7D%2A2x%3D)
![\frac{6xtg^2(x^2+1)}{cos^2(x^2+1)}= \frac{6xsin^2(x^2+1)}{cos^4(x^2+1)}](https://tex.z-dn.net/?f=+%5Cfrac%7B6xtg%5E2%28x%5E2%2B1%29%7D%7Bcos%5E2%28x%5E2%2B1%29%7D%3D+%5Cfrac%7B6xsin%5E2%28x%5E2%2B1%29%7D%7Bcos%5E4%28x%5E2%2B1%29%7D)
</span>