1) y = 2x⁵ - x
y' = 2(x⁵)' - x' = 10x⁴ - 1
2) y = - 3Sinx + 2Cosx
y' = - 3(Sinx)' + 2(Cosx)' = - 3Cosx - 2Sonx
3) y = 2/3x³ - x² - 7x
y' = 2/3(x³)' - (x²)' - 7(x)' = 2/3 * 3x² - 2x - 7 = 2x² - 2x - 7
4) y = (x + 2)(x² - 7x + 5)
y' = (x + 2)' * (x² - 7x + 5) + (x + 2)(x² - 7x + 5)' = 1 * (x² - 7x + 5) +
+ (x + 2)(2x - 7) = x² - 7x + 5 + 2x² - 7x + 4x - 14 = 3x² - 10x - 9
5) y = x² Sinx
y' = (x² )' * Sinx + x² * (Sinx)' = 2xSinx + x²Cosx
6) y = (3x - 5)⁶
y' = [(3x - 5)⁶]' = 6(3x - 5)⁵ * (3x - 5)' = 18(3x - 5)⁵
7)
![y=Sin \frac{x}{3}\\\\y'=(Sin \frac{x}{3} )'= Cos \frac{x}{3}*( \frac{x}{3})'= \frac{1}{3} Cos \frac{x}{3}](https://tex.z-dn.net/?f=y%3DSin+%5Cfrac%7Bx%7D%7B3%7D%5C%5C%5C%5Cy%27%3D%28Sin+%5Cfrac%7Bx%7D%7B3%7D+%29%27%3D+Cos+%5Cfrac%7Bx%7D%7B3%7D%2A%28+%5Cfrac%7Bx%7D%7B3%7D%29%27%3D+%5Cfrac%7B1%7D%7B3%7D+Cos+%5Cfrac%7Bx%7D%7B3%7D+++)
8)
![y = (9x - 2) ^{-3} \\\\y'=[(9x-2) ^{-3}]'=-3(9x-2) ^{-4} *(9x-2)'= -27(9x-2) ^{-4}](https://tex.z-dn.net/?f=y+%3D+%289x+-+2%29+%5E%7B-3%7D+%5C%5C%5C%5Cy%27%3D%5B%289x-2%29+%5E%7B-3%7D%5D%27%3D-3%289x-2%29+%5E%7B-4%7D+%2A%289x-2%29%27%3D+-27%289x-2%29+%5E%7B-4%7D++)