| x | 2+x | |||
a) | = | |||
| √1+x | 2√1+x3 |
| x | 1 | ||||||||||||
b) arcsin(log | )= | ||||||||||||
| 10 |
|
| 2+2x2+√1+x2 | ||
c) arctg(x+√1+x2)= | ||
| 2(1+x2) |
| x | ||
f(x)= | ||
| √x+1 |
| 2(x+1)−x | ||||||||||||
f '(x)= | = | = | |||||||||||
| (x+1) | 2*(x+1)*√x+1 |
| x+2 | ||
= | ||
| 2*(x+1)√x+1 |
| 1 | ||
c) (arctg(x+√1+x2)'= | *(x+√1+x2)'= | |
| 1+(x+√1+x2)2 |
| 1 | 2x | |||
= | *(1+ | )= | ||
| 1+x2+2x√1+x2+1+x2 | 2*√(1+x2) |
| 1 | √1+x2+x | |||
= | * | i można zostawić, albo dalej tak : | ||
| 2*(x2+x√1+x2+1) | √1+x2 |
| 1 | √1+x2+x | √x2+1 | ||||
= | * | * | = | |||
| 2*(x2+x√1+x2+1) | √1+x2 | √x2+1 |
| 1 | 1+x2+x√x2+1 | 1 | ||||
= | * | = | ||||
| 2*(x2+x√1+x2+1) | (x2+1) | 2*(x2+1) |
| 5^2 | 52 |
| 2^{10} | 210 |
| a_2 | a2 |
| a_{25} | a25 |
| p{2} | √2 |
| p{81} | √81 |
| Kliknij po więcej przykładów | |
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