Question

Помогите по производным.

Answer 1

Ответ:

Пошаговое объяснение:

2 . 1) f( x ) = x⁴ ;    f '( x ) = ( x⁴ )' = 4x³ ;

    2)  f( x ) = 5x⁵ ;     f '( x ) = 5 * 5x⁴ = 25x⁴ ;

    3)  f( x ) = x⁷ + 2 ;     f '( x ) = ( x⁷ + 2 )' = 7x⁶ + 0 = 7x⁶ ;

4)  f( x ) = - 5/x⁶ = - 5x⁻⁶ ;     f '( x ) = -5 * (- 6 )x⁻⁷ = 30/x⁷ ;

5)  f( x ) = ( 5 - 2x )/(2 - 3x ) = ( 2x - 5 )/( 3x - 2 ) ;   f '( x ) = [ 2( 3x - 2 ) -

   - 3( 2x - 5 )] /( 3x - 2 )² = ( 6x - 4 - 6x + 15 )/( 3x - 2 )² = 11/( 3x - 2 )² ;

6)  f( x ) = - 8 + ln( lnx ) ;   f '( x ) = (- 8 )' + [ ln( lnx ) ]' = 0 + 1/lnx * ( lnx )' =

    = 1/lnx * 1/x = 1/( x lnx ) ;   7)  f( x ) = x³ * x = x⁴ ;   f '( x ) = ( x⁴ )' = 4x³ ;

8)  f( x ) = - 5cosx ;    f '( x ) = - 5 *( cosx )' = - 5 *(- sinx ) = 5sinx ;

9)    f( x ) = eˣ tgx ;     f '( x ) = ( eˣ )' tgx + eˣ *( tgx )' = eˣ tgx + eˣ * 1/cos²x =

              = eˣ ( tgx + 1/cos²x ) .