13 uždavinys

12 uždavinys14 uždavinys

f(x) = $\sqrt {2}\cdot x^{2}+\sqrt {2}$ . Apskaičiuokite f'(√2)

Sprendimas.

( saknis(

2)* x^²+saknis(

2))′ =

( saknis(

2)* x^²+saknis(

2))′ = $(\sqrt {2}\cdot x^{2}+\sqrt {2})'$ =

( saknis(

2)* x^²)′ = $(\sqrt {2}\cdot x^{2})'$ =

saknis(

2)* saknis(

2)* 2 = $\sqrt {2}\cdot \sqrt {2}\cdot 2$ =

$(\sqrt {2}\cdot x^{2}+\sqrt {2})'$ =

$(\sqrt {2}\cdot x^{2})'+\sqrt {2}'$ =

$(\sqrt {2}\cdot x^{2})'$ =

$\sqrt {2}\cdot 2\cdot x$ =

$\sqrt {2}\cdot 2\cdot \sqrt {2}$ =

$4$

Atsakymas: 4

12 uždavinys14 uždavinys