| 1 − t1/2 | ||
y(t) = ( | )1/2 | |
| 1 + t1/2 |
| v | ||
y(t) = u1/2 u(t) = | v(t) = 1 − t1/2 w(t) = 1 + t1/2} | |
| w |
| 1 | ||
y'(t) = (u(t)1/2)' = (√u(t))' = | * u'(t) = [1] | |
| 2√u(t) |
| v(t) | v'(t)w(t) − v(t)*w'(t) | |||
u'(t) = ( | )' = | = [2] | ||
| w(t) | v2(t) |
| 1 | 1 | |||
v'(t) = (1 − t1/2)' = (1 − √t)' = − | * t' = − | |||
| 2√t | 2√t |
| 1 | 1 | |||
w'(t) = (1 + t1/2})' = (1 + √t)' = | * t' = | |||
| 2√t | 2√t |
| v'(t)w(t) − v(t)*w'(t) | ||
[2] = | = | |
| v2(t) |
| |||||||||||||||||
= | = uprościć | ||||||||||||||||
| (1 − t1/2)2 |
| 1 | ||
[1] = | * u'(t) = | |
| 2√u(t) |
| 1 | ||
= | * [2] = podstawić wynik z [2] i | |
| 2√(1 − t1/2/1 + t1/2)1/2 |