Упр.303 ГДЗ Колягин Ткачёва 11 класс (Алгебра)
1) f(x) = sin2x;
2) f(x) = x3sinx;
3) f(x) = x4 + 3х2 — x + 1;
4) f(x) = x4 — 3×3 + 5x + 6;
5) f(x) = esinx;
6) f(x) = ln(x2 + 1).
$$f(x)=\sin^2 x$$
$$f'(x)=2\sin x\cos x=\sin 2x$$
$$f»(x)=2\cos 2x$$
$$f(x)=x^3\sin x$$
$$f'(x)=3x^2\sin x+x^3\cos x$$
$$f»(x)=6x\sin x+3x^2\cos x+3x^2\cos x-x^3\sin x$$
$$f»(x)=(6x-x^3)\sin x+6x^2\cos x$$
$$f(x)=x^4+3x^2-x+1$$
$$f'(x)=4x^3+6x-1$$
$$f»(x)=12x^2+6$$
$$f(x)=x^4-3x^3+5x+6$$
$$f'(x)=4x^3-9x^2+5$$
$$f»(x)=12x^2-18x$$
$$f(x)=e^{\sin x}$$
$$f'(x)=e^{\sin x}\cos x$$
$$f»(x)=e^{\sin x}\cos^2 x-e^{\sin x}\sin x$$
$$f»(x)=e^{\sin x}\left(\cos^2 x-\sin x\right)$$
$$f(x)=\ln(x^2+1)$$
$$f'(x)=\frac{2x}{x^2+1}$$
$$f»(x)=\frac{2(x^2+1)-4x^2}{(x^2+1)^2}$$
$$f»(x)=\frac{2(1-x^2)}{(x^2+1)^2}$$
Ответ
$$1)\ f»(x)=2\cos 2x;\quad 2)\ f»(x)=(6x-x^3)\sin x+6x^2\cos x;\quad 3)\ f»(x)=12x^2+6;$$
$$4)\ f»(x)=12x^2-18x;\quad 5)\ f»(x)=e^{\sin x}\left(\cos^2 x-\sin x\right);\quad 6)\ f»(x)=\frac{2(1-x^2)}{(x^2+1)^2}.$$
