Упр.953 ГДЗ Алимов 10-11 класс (Алгебра)
1) f (x) = х2 cos x;
2) f (x) = x3 sin x;
3) f (x) = x5 + 2×3 — x2 + 2;
4) f (x) = x4 — 3х3 + 5x + 6.
$$f(x)=x^2\cos x$$
Найдём вторую производную:
$$ f'(x)=(x^2)’\cos x+x^2(\cos x)’=2x\cos x-x^2\sin x $$
$$ f»(x)=(2x\cos x)’-(x^2\sin x)’=2\cos x-2x\sin x-2x\sin x-x^2\cos x $$
$$ f»(x)=(2-x^2)\cos x-4x\sin x $$
$$f(x)=x^3\sin x$$
$$ f'(x)=(x^3)’\sin x+x^3(\sin x)’=3x^2\sin x+x^3\cos x $$
$$ f»(x)=(3x^2\sin x)’+(x^3\cos x)’=6x\sin x+3x^2\cos x+3x^2\cos x-x^3\sin x $$
$$ f»(x)=(6x-x^3)\sin x+6x^2\cos x $$
$$f(x)=x^5+2x^3-x^2+2$$
$$ f'(x)=5x^4+6x^2-2x $$
$$ f»(x)=20x^3+12x-2 $$
$$f(x)=x^4-3x^3+5x+6$$
$$ f'(x)=4x^3-9x^2+5 $$
$$ f»(x)=12x^2-18x $$
Ответ
1) $$f»(x)=(2-x^2)\cos x-4x\sin x$$
2) $$f»(x)=(6x-x^3)\sin x+6x^2\cos x$$
3) $$f»(x)=20x^3+12x-2$$
4) $$f»(x)=12x^2-18x$$
