Задача 48766 ...

sova

2020-04-29 08:07:48

★

[m]dy=y`(x)dx[/m]

[m](\frac{u}{v})`=\frac{u`\cdot v-u\cdot v`}{v^2}[/m]


[m]y`=\frac{(tgx-5x)`\cdot e^{arcsinx}-(tgx-5x)\cdot (e^{arcsinx})`}{(e^{arcsinx})^2}[/m]

[m]y`=\frac{(\frac{1}{cos^2x}-5)\cdot e^{arcsinx}-(tgx-5x)\cdot e^{arcsinx}\cdot (arcsinx)`}{(e^{arcsinx})^2}[/m]

[m]y`=\frac{(\frac{1}{cos^2x}-5)\cdot e^{arcsinx}-(tgx-5x)\cdot e^{arcsinx}\cdot \frac{1}{\sqrt{1-x^2}}}{(e^{arcsinx})^2}[/m]

[m]dy=\frac{\frac{1}{cos^2x}-5- \frac{tgx-5x}{\sqrt{1-x^2}}}{e^{arcsinx}}dx[/m]