Ксения Райт
Гений
(93544)
2 месяца назад
1) y' = [4·x^(-3)+x^(7/5)]' =
-12·x^(-4)+1,4·x^(2/5) = -12/x⁴+1,4·⁵√x²
y'(1) = -12 + 1,4 = -10,6
2) y' = [(e⁴ˣ-x)'·(x⁵-2)-(e⁴ˣ-x)·(x⁵-2)']/(x⁵-2)² =
[(4e⁴ˣ-1)(x⁵-2)-(e⁴ˣ-x)·5x⁴]/(x⁵-2)² =
[(4x⁵-5x⁴-8)·e⁴ˣ+4x⁵+2]/(x⁵-2)²
y'(0) = (-8+2)/4 = -1,5
3) y' = [√(x³+1)]'/[1+√(x³+1)²] =
[1,5x²/√(x³+1)]·(x³+2) =
1,5x²/[(x³+2)√(x³+1)]
y'(1) = 1,5/(3√2) = ¼·√2