1.1 f'(x)=15x²-16x³+4x-3 f'(1)=15-16+4-3=0
1.2 f(x)=xctgx f'(x)=(uv)'=u'v+v'u u=x u'=1 v=ctgx v'=-1/sin²x
f'(x)=1*ctgx-x/sin²x f'(π/4)=1-(π/4)/(1/√2)²=1-2π/4=1-π/2
2a f'(u/v)=1/v²[u'v-v'u] u=3x-2 u'=3 v=2x+3 v'=2
f'(x)=1/(2x+3)²[3(2x+3)+2(3x-2)]
2b f(x)=7*x^6/7 f'(x)=7*6/7x^(6/7-1)=6x^(-1/7)=6/x^(1/7)
2c f(x)=√(6x+5) f'(x)=6/2√(6x+5) = 3/√(6x+5)
<span>a)a^5*a^3 =a^(5+3)=a^8
б) a^8:a^6 =a^(8-6)=a^2
в) (a^2)^4=a^(2*4)=a^8
г) (ab)^6 =a^6b^6
д) (a/b)^3-a^3/b^3</span>
(5А²-2А-3)-(2А²+2А-5)=
=5А²-2А-3-2А²-2А+5=
=3А²-4А+2
2-6x<0
-6x<-2
x>2/6
x>1/3
Ответ: 3) x>1/3
<span>1. Представьте в виде квадрата двучлена трехчлены:
1) z² + 1,4z + 0,49=(z+0,7)</span>²<span>
2) 2,25 - 3x + x²=(1,5-x)</span>²<span>
3) 3,61 + 3,8d + d²=(1,9+d)</span>²<span>
2. Упростите выражения:
1) (m + 8)² - (m - 2n) ⋅ (m + 2n)=m</span>²+16m+64-m²+4n²=16m+64+4n²<span>
2) (n + 15)² - n ⋅ (n - 19)=n</span>²+30n+225-n²+19n=49n+225<span>
3) (6 - 5m) ⋅ (5m + 6) + (5m - 4)²=36-25m</span>²<span>+25m</span>²-40m+16=52-40m