Funkcijos isvestine ir jos taikymai

Rasti funkcijos isvestine:

1)  f(x) = sin²(4x)

2)  f(x) = cos² x/2


3) 

Prasau padeti isspresti siuos uzdavinius.

1)[tex]${\left[ {({{\sin }^2}(4x))} \right]^\prime } = {\left[ {{{(\sin (4x))}^2}} \right]^\prime } = 2\sin (4x) \cdot {\left[ {\sin (4x)} \right]^\prime } = $[/tex][tex]$ = 2\sin (4x) \cdot \left( {\cos (4x) \cdot (4x)'} \right) = 8\sin (4x)\cos (4x) = 4\sin (8x)$[/tex]

2)[tex]\[{\left[ {{{\cos }^2}(\frac{x}{2})} \right]^\prime } = {\left[ {{{\left( {\cos (\frac{x}{2})} \right)}^2}} \right]^\prime } = 2\cos (\frac{x}{2}) \cdot  - \sin (\frac{x}{2}) \cdot \frac{1}{2} = \]
[/tex][tex]\[ - \cos (\frac{x}{2})\sin (\frac{x}{2}) =  =  - \frac{{\sin (x)}}{2}\]
[/tex]

3) analogiškai