F(x)=0,5 ^x cos 2x , x0= 0

F ( x ) = 0,5 ^ x * cos 2x при x0 = 0 ;
Производная F ( x ) = ( 0,5 ^ x * cos 2x ) \' = ( 0.5 ^ x ) \' * cos 2x + 0.5 ^ x * ( cos 2x ) \' = ( 0.5 ^ x ) \' * cos 2x + 0.5 ^ x * ( cos 2x ) \' = 0.5 ^ x * ln ( 0.5 ) * cos 2x + 0.5 ^ x * ( - sin 2x ) * ( 2 * x )\' = 0.5 ^ x * ln ( 0.5 ) * cos 2x + 0.5 ^ x * ( - sin 2x ) * 2 = 0.5 ^ x * ln ( 0.5 ) * cos 2x - 2 * 0.5 ^ x * sin 2x ;
При х0 = 0, Производная F ( 0 ) = 0.5 ^ 0 * ln ( 0.5 ) * cos ( 2* 0) - 2 * 0.5 ^ 0 * sin ( 2 * 0 ) = 1 * ln ( 0.5 ) * 1 - 2 * 1 * 0 = ln ( 0.5 ).