






! Pochodne
| 1 − e−x | ||
1) | ||
| 1 + ex |
| 1 − e− | ||
f(x) = | ||
| 1 + ex |
| ( 1 − e−x)'( 1 + ex) − ( 1 − e−x)*( 1 + ex)' | ||
f ' (x) = | = | |
| ( 1 + ex)2 |
| ex *( 1 + ex) − (1 − e−x)*(ex) | ||
= | = | |
| ( 1 + ex)2 |
| ex − ( ex)2 − ex + e0 | 1 − e2x | |||
= | = | |||
| ( 1 + ex)2 | ( 1 + ex)2 |
Od drugiego wiersza powinno być
| e−x *( 1 + ex) − ( 1 − e−x)*ex | ||
= | = | |
| ( 1 + ex)2 |
| e−x + e0 − ex + e0 | 2 + e−x − ex | |||
= | = | |||
| ( 1 + ex)2 | ( 1 + ex)2 |