x2 − x + 1 | ||
f(x) = | ||
x2 + x + 1 |
( 2 x − 1)*( x2 + x + 1) − ( x2 − x + 1)*( 2 x + 1) | ||
f '(x) = | = ... | |
( x2 + x + 1)2 |
x2 − x + 1 | ||
y = | ||
x2 + x + 1 |
u | ||
y = | u = x2 − x + 1 v = x2 + x + 1 | |
v |
u | u'v − uv' | |||
y' = [ | ]' = | = *) | ||
v | v2 |
(2x − 1)(x2 + x + 1) − (x2 − x + 1)(2x + 1) | ||
*) = | = | |
(x2 + x + 1)2 |
2x3 + 2x2 + 2x − x2 − x − 1 − (2x3 + x2 − 2x2 − x + 2x + 1) | ||
= | = | |
(x2 + x + 1)2 |
2x3 + 2x2 + 2x − x2 − x − 1 − 2x3 − x2 + 2x2 + x − 2x − 1 | ||
= | = | |
(x2 + x + 1)2 |
2x2 − 2 | ||
= | ||
(x2 + x + 1)2 |