4.63
д) f(x)= 1 = x^(-1/3)
∛x
f(x)' = - 1
3x ∛x
e) f(x)= 1 = x^(-2/3)
∛x²
f(x)' = -2 x^(-5/3) = -2
3 3x ∛x²
ж) f(x)=x² √x =x^(3/2)
f(x)' = 3√x = 1.5√x
2
з) f(x) = x³ = x^(3 - 1/3) = x^(8/3)
∛x
f(x)' = 8 x^(5/3) = 8x ∛x²
3 3
4.64
a) f(x)=√(x²-3x+10)
f(x)' = 2x-3
2√(x²-3x+10)
д) f(x)=∛(x²-6x+9) = ∛(x-3)² = (x-3)^(2/3)
f(x)' = 2
3 ∛(x-3)
4.67
б) y=(x+5)²¹
y' = 21(x+5)²⁰
x₁= -6 y' (-6)= 21(-6+5)²⁰ =21*(-1)²⁰ =21*1=21
x₂= -4 y' (-4)= 21(-4+5)²⁰ =21*1²⁰ =21*1=21
г) y=(2x-3)¹⁰⁰¹
y'=1001 (2x-3)¹⁰⁰⁰ * 2 = 2002* (2x-3)¹⁰⁰⁰
x₁=1 y' (1)= 2002 * (2-3)¹⁰⁰⁰ = 2002*(-1)¹⁰⁰⁰=2002
x₂=2 y' (2)= 2002 * (2*2-3)¹⁰⁰⁰=2002 * 1¹⁰⁰⁰ = 2002