Упр.248 ГДЗ Колягин Ткачёва 11 класс (Алгебра)

2) 1/4×2-ex + 2sin x;
3) 15 корень 5 степени x+ ex — 6tgx;
4) 6 корень 6 степени x — lnx + 1/3cosx;
5) x2(x — 1) + 3 sinx + 4 ctgx;
6) x (x + 2)2 + 2lnx- 3 cosx;
7) (x — 1)(x + 2) + ex — lnx;
8) (x + 3)(2x — 1) + ex — sinx.

1. $$y=\frac{1}{5}x^2+2\ln x-\cos x$$

   $$y’=\frac{1}{5}\cdot 2x+2\cdot \frac{1}{x}-(-\sin x)=\frac{2}{5}x+\frac{2}{x}+\sin x$$

2. $$y=\frac{1}{4}x^2-e^x+2\sin x$$

   $$y’=\frac{1}{4}\cdot 2x-e^x+2\cos x=\frac{1}{2}x-e^x+2\cos x$$

3. $$y=15\sqrt[5]{x}+e^x-6\tg x$$

   $$y’=15\cdot \frac{1}{5}x^{-\frac{4}{5}}+e^x-6\cdot \frac{1}{\cos^2 x}$$

   $$y’=\frac{3}{\sqrt[5]{x^4}}+e^x-\frac{6}{\cos^2 x}$$

4. $$y=6\sqrt[6]{x}-\ln x+\frac{1}{3}\cos x$$

   $$y’=6\cdot \frac{1}{6}x^{-\frac{5}{6}}-\frac{1}{x}+\frac{1}{3}(-\sin x)$$

   $$y’=\frac{1}{\sqrt[6]{x^5}}-\frac{1}{x}-\frac{1}{3}\sin x$$

5. $$y=x^2(x-1)+3\sin x+4\ctg x$$

   $$y’=(x^2)'(x-1)+x^2(x-1)’+3\cos x+4(\ctg x)’$$

   $$y’=2x(x-1)+x^2+3\cos x-4\cdot \frac{1}{\sin^2 x}$$

   $$y’=3x^2-2x+3\cos x-\frac{4}{\sin^2 x}$$

6. $$y=x(x+2)^2+2\ln x-3\cos x$$

   $$y’=(x)'(x+2)^2+x\bigl((x+2)^2\bigr)’+2\cdot \frac{1}{x}-3(-\sin x)$$

   $$y’=(x+2)^2+2x(x+2)+\frac{2}{x}+3\sin x$$

   $$y’=3x^2+8x+4+\frac{2}{x}+3\sin x$$

7. $$y=(x-1)(x+2)+e^x-\ln x$$

   $$y’=(x-1)'(x+2)+(x-1)(x+2)’+e^x-\frac{1}{x}$$

   $$y’=(x+2)+(x-1)+e^x-\frac{1}{x}$$

   $$y’=2x+1+e^x-\frac{1}{x}$$

8. $$y=(x+3)(2x-1)+e^x-\sin x$$

   $$y’=(x+3)'(2x-1)+(x+3)(2x-1)’+e^x-\cos x$$

   $$y’=(2x-1)+2(x+3)+e^x-\cos x$$

   $$y’=4x+5+e^x-\cos x$$

Ответ

1. $$y’=\frac{2}{5}x+\frac{2}{x}+\sin x$$
2. $$y’=\frac{1}{2}x-e^x+2\cos x$$
3. $$y’=\frac{3}{\sqrt[5]{x^4}}+e^x-\frac{6}{\cos^2 x}$$
4. $$y’=\frac{1}{\sqrt[6]{x^5}}-\frac{1}{x}-\frac{1}{3}\sin x$$
5. $$y’=3x^2-2x+3\cos x-\frac{4}{\sin^2 x}$$
6. $$y’=3x^2+8x+4+\frac{2}{x}+3\sin x$$
7. $$y’=2x+1+e^x-\frac{1}{x}$$
8. $$y’=4x+5+e^x-\cos x$$