Question

Похідні:
1. y= 2x5(степінь)-x
2. y= -3sinx+2cosx
3. y= 2/3x³-x²-7x
4. y= (x+2)(x²-7x+5)
5. y= x²sinx
6. y= (3x-5)6(степінь)
7. y= sinx/3
8. y= (9x-2)-3(степінь)

Answer 1

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) $y=Sin \frac{x}{3}\\\\y'=(Sin \frac{x}{3} )'= Cos \frac{x}{3}*( \frac{x}{3})'= \frac{1}{3} Cos \frac{x}{3}$

8) $y = (9x - 2) ^{-3} \\\\y'=[(9x-2) ^{-3}]'=-3(9x-2) ^{-4} *(9x-2)'= -27(9x-2) ^{-4}$