Упр.871 ГДЗ Алимов 10-11 класс (Алгебра)

2) e2x — ln 3x;
3) sin (x — 3) — ln (1 — 2x);
4) 6 sin2x/3 — -e^(1-3x).

1. $$f(x)=\sin 5x+\cos(2x-3)$$
   $$f'(x)=(\sin 5x)’+(\cos(2x-3))’$$
   $$f'(x)=5\cos 5x-2\sin(2x-3)$$
2. $$f(x)=e^{2x}-\ln 3x$$
   $$f'(x)=(e^{2x})’-(\ln 3x)’$$
   $$f'(x)=2e^{2x}-\frac{1}{x}$$
3. $$f(x)=\sin(x-3)-\ln(1-2x)$$
   $$f'(x)=(\sin(x-3))’-(\ln(1-2x))’$$
   $$f'(x)=\cos(x-3)+\frac{2}{1-2x}$$
4. $$f(x)=6\sin\frac{2x}{3}-e^{1-3x}$$
   $$f'(x)=6\left(\sin\frac{2x}{3}\right)’-(e^{1-3x})’$$
   $$f'(x)=6\cdot\frac{2}{3}\cos\frac{2x}{3}+3e^{1-3x}$$
   $$f'(x)=4\cos\frac{2x}{3}+3e^{1-3x}$$

Ответ

1. $$5\cos 5x-2\sin(2x-3)$$
2. $$2e^{2x}-\frac{1}{x}$$
3. $$\cos(x-3)+\frac{2}{1-2x}$$
4. $$4\cos\frac{2x}{3}+3e^{1-3x}$$