Задача 9 (Похідна складеної функції)

Обчислити похідну функції  y = arcsin\: e^{x}-\sqrt{1-e^{2x}}

 y' = (arcsin\: e^{x}-\sqrt{1-e^{2x}})'=

 =(arcsin\: e^{x})'-(\sqrt{1-e^{2x}})'=

 =\frac{1}{\sqrt{1-e^{2x}}}\cdot (e^{x})'-\frac{1}{2\sqrt{1-e^{2x}}}\cdot \left(1-e^{2x} \right)=

 =\frac{e^{x}}{\sqrt{1-e^{2x}}}-\frac{1}{2\sqrt{1-e^{2x}}}\cdot \left(-2e^{2x} \right)=

 =\frac{1}{\sqrt{1-e^{2x}}}\left(e^{x}+e^{2x} \right)=\frac{e^{x}+e^{2x}}{\sqrt{1-e^{2x}}}

2 Responses to “Задача 9 (Похідна складеної функції)”

  • nike shoes says:

    I must show my appreciation for your kind-heartedness giving support to women who really want help on your topic. Your special dedication to getting the solution across was amazingly interesting and have consistently helped men and women just like me to arrive at their objectives. The insightful report denotes a great deal to me and somewhat more to my fellow workers. Thanks a ton; from everyone of us.

  • I’m also commenting to make you know what a magnificent encounter my friend’s child had reading through your web site. She discovered plenty of details, which include what it is like to possess a wonderful teaching style to have many others easily thoroughly grasp specific extremely tough issues. You actually surpassed her desires. Thank you for presenting those interesting, dependable, informative as well as unique tips on your topic to Kate.

Leave a Reply

Зараз на сайті
contador de visitas счетчик посещений
Лічильник сайту
html counterсчетчик посетителей сайта
Травень 2019
Пн Вт Ср Чт Пт Сб Нд
« Кві