Y`=(4x⁵+x²)`(3x²-5x+1)+<span>(4x⁵+x²)(3x²-5x+1)`=</span>(20x⁴+2x)(3x²-5x+1)+(4x⁵+x²)(6x-5)=60x⁶+6x³-100x⁵-10x²+20x⁴+2x+24x⁶+6x³-20x⁵-5x²=84x⁶-120x⁵+20x⁴+12x³-15x²+2x
ОДЗ
{x+1>0⇒x>-1
{x+1≠1⇒x≠0
{x-1>0⇒x>1
{x+2>0⇒x>-2
x∈(1;∞)
1){log(x+1)(x-1)≥0⇒x-1≥1⇒x≥2
{log(x+1)(x+2)≤0⇒x+2≤1⇒x≤-1
нет решения
2){log(x+1)(x-1)≤0⇒x-1≤1⇒x≤2
{log(x+1)(x+2)≥0⇒x+2≥1⇒x≥-1
-1≤х≤2 +ОДЗ⇒x∈(1;2]
Y = 1/(x^2 + 1) = (x^2 + 1)^(-1)
y ' = - 1 * (x^2 + 1)^ (-2) * (x^2 + 1) ' =
= - (x^ 2 + 1)^( -2) * 2x = - 2x/ (x^2 + 1)^2
U = arccos (- 4/5)
v = arcsin 1/3
sin(u + v) = sin(arccos (- 4/5)).cos(arcsin 1/3) + cos(arccos (- 4/5)).sin(arcsin (1/3)) =
= √[1 – (- 4/5)²] * √[1 – (1/3)²] + (- 4/5)*(1/3) = √[1 – 16/25] * √[1 – 1/9] - 4/15 =
= √[(9/25)*(8/9)] – 4/15 = (2√2) / 5 - 4/15 = (6√2 - 4) / 15