Ответ:1).14; 2).1; 3).35; 4).√2(1-π/4)
Пошаговое объяснение:
1).f ′ (x)=8x+6. f ′ (1)=8+6=14
2).f ′ (x)=(x/(1+x²))′ =(1·(1+x²)-x·2x)/(1+x²)²=(1+x²-2x²)/(1+x²)²=(1-x²)/(1+x²)²
f′ (0)=(1-0)²/(1+0²)²=1
3).f (x)=(3x²-1)·(3x²+1)=9x⁴-1. f ′ (x)=36x³-1.f ′ (1)=36·1⁴-1=36-1=35
4).f ′ (x)=2·cosx+2x·(-sinx)=2cosx-2x·sinx=2(cosx-x·sinx)
f ′ (π/4)=2·(√2/2-π/4·√2/2)=√2(1-π/4)