Упр.207 ГДЗ Колягин Ткачёва 11 класс (Алгебра)

2) ln(3-4×2);
3) e^2/x+1;
4) e^1/2x+3;
5) ln 2/3-4×2;
6) ln 3/2×2+7x.

1. $$y=e^{\frac{1}{x-1}}$$
   $$y’ = e^{\frac{1}{x-1}} \cdot \left(\frac{1}{x-1}\right)’ = e^{\frac{1}{x-1}} \cdot \left(-(x-1)^{-2}\right)$$
   $$y’=-\frac{e^{\frac{1}{x-1}}}{(x-1)^2}$$
2. $$y=\ln(3-4x^2)$$
   $$y’=\frac{(3-4x^2)’}{3-4x^2}=\frac{-8x}{3-4x^2}$$
   $$y’=\frac{8x}{4x^2-3}$$
3. $$y=e^{\frac{2}{x+1}}$$
   $$y’=e^{\frac{2}{x+1}}\cdot \left(\frac{2}{x+1}\right)’=e^{\frac{2}{x+1}}\cdot \left(-\frac{2}{(x+1)^2}\right)$$
   $$y’=-\frac{2e^{\frac{2}{x+1}}}{(x+1)^2}$$
4. $$y=e^{\frac{1}{2x+3}}$$
   $$y’=e^{\frac{1}{2x+3}}\cdot \left(\frac{1}{2x+3}\right)’=e^{\frac{1}{2x+3}}\cdot \left(-\frac{2}{(2x+3)^2}\right)$$
   $$y’=-\frac{2e^{\frac{1}{2x+3}}}{(2x+3)^2}$$
5. $$y=\ln\frac{2}{3-4x^2}$$
   $$y’=\frac{\left(\frac{2}{3-4x^2}\right)’}{\frac{2}{3-4x^2}}$$
   $$\left(\frac{2}{3-4x^2}\right)’=\frac{8x}{(3-4x^2)^2}$$
   $$y’=\frac{8x}{2(3-4x^2)}=\frac{4x}{3-4x^2}$$
6. $$y=\ln\frac{3}{2x^2+7x}$$
   $$y’=\frac{\left(\frac{3}{2x^2+7x}\right)’}{\frac{3}{2x^2+7x}}$$
   $$\left(\frac{3}{2x^2+7x}\right)’=-\frac{3(4x+7)}{(2x^2+7x)^2}$$
   $$y’=-\frac{4x+7}{2x^2+7x}$$

Ответ

$$1)\; y’=-\frac{e^{\frac{1}{x-1}}}{(x-1)^2};\quad 2)\; y’=\frac{8x}{4x^2-3};\quad 3)\; y’=-\frac{2e^{\frac{2}{x+1}}}{(x+1)^2};$$
$$4)\; y’=-\frac{2e^{\frac{1}{2x+3}}}{(2x+3)^2};\quad 5)\; y’=\frac{4x}{3-4x^2};\quad 6)\; y’=-\frac{4x+7}{2x^2+7x}.$$