Решение
1) (x¹⁰)` = 10x⁹
2) (-7x⁶) `= - 42x⁵
3) (7x⁷ - 3x⁵ - 8x + 217)` = 49x⁶ - 15x⁴ - 8
4) (x⁶ + 13)*(x⁴ + 1) = x¹⁰ + x⁶ + 13x⁴ + 13
(x¹⁰ + x⁶ + 13x⁴ + 13)` = 10x⁹ + 6x⁵ + 52x³
5) (cos5x)` = - 5sin5x
6) (sinx)` = cosx
7) (cosx + tgx)` = - sinx + 1/cos²x
8) (x⁶ - 2x³ + 5x)` = 6x⁵ - 6x² + 5
f(-1) = 6*(-1)⁵ - 6*(-1)² + 5 = - 6 - 6 + 5 = - 7
9) (-24x² + 3x³)` < 0
- 48x + 9x² < 0
9x² - 48x < 0
x(9x - 48) < 0
x(9x - 48) = 0
x = 0 9x - 48 = 0
x = 48/9, x = 5(1/3)
+ - +
-------------------------------------------->
0 5(1/3) x
x ∈ (0; 5(1/3)
10) f(x) = 15x² - 18x + 1171 f`(x) = 0
f`(x) = 30x - 18
30x - 18 = 0
30x = 18
x = 18/30
x = 3/5