Pochodna w punkcie
x: Oblicz wartość pochodnej funkcji f(x)=x/(x−1)2 w punkcie x=−3.
13 mar 18:03
ICSP: | | x | | 1 | | 1 | |
f(x) = |
| = |
| + |
| |
| | (x−1)2 | | (x−1)2 | | x − 1 | |
| | −2 | | 1 | |
f'(x) = |
| − |
| |
| | (x−1)3 | | (x−1)2 | |
f(−3) = ...
13 mar 18:05
Benny: Pochodna ilorazu
| | f(x) | | f'(x)*g(x) − f(x)*g'(x) | |
( |
| )'= |
| |
| | g(x) | | g(x)2 | |
13 mar 18:05
pigor: ...., np. z pochodnej iloczynu :
f '(x) = (x (x−1)
−2) ' =1*(x−1)
−2+x*(−2)(x−1)
−3=
| | −x−1 | | x+1 | |
= (x−1)−3(x−1−2x)= |
| = |
| . ..  |
| | (x−1)3 | | (1−x)3 | |
13 mar 18:14
pigor: ..., więc
| | −3+1 | | −2 | | −1 | | 1 | |
f '(−3) = |
| = |
| = |
| = − |
| |
| | (1+3)3 | | 4*42 | | 2*16 | | 32 | |
13 mar 18:17