Презентации по математике / Презентации / 09.Дифференциальное исчисление

6. y = sin6X , y’ - ?

y’ = (sin6X)’ = (sinU)’ = cosU . U’ = cos6X . (6X)’ = 6

cos6X

7. y = (1+5x)3 , y’ - ?

y’ = ((1 + 5x)3)’ = (U3)’ = 3U2 . U’ = 3(1+5x)2 . (1+5x)’ =

= 15 . (1+5x)2

8. (cos2X)’ = ((cosX)2)’ = (U2)’ = 2U . U’ = 2cosX . (cosX)’

=

= - 2cosX . sinX = - sin2X

9. (esinX2)’ = (eU)’ = eU . U’ = esinX2 . (sinX2)’ = esinX2 .

(sinU)’ =