Question

ПОМОГИТЕ РЕШИТЬ
найти производную функции:
(5х+3х)³(2х-1)⁴

Answer 1

(u*v)`=u`·v+u·v`

u=(5x+3)³

u`=3·(5x+3)²·(5x+3)`=3·(5x+3)²·5=15·(5x+3)²

v=(2x-1)⁴

v`=4·(2x-1)³·(2x-1)`=4·(2x-1)³·2=8·(2x-1)³

((5x+3)³·(2x-1)⁴)=((5x+3)³)`·(2x-1)⁴+(5x+3)³·((2x-1)⁴)`=

=15·(5x+3)²·(2x-1)⁴+(5x+3)³·8·(2x-1)³=

=(5x+3)²·(2x-1)³·(15·(2x-1)+8·(5x+3))=

=(5x+3)²·(2x-1)³·(30x-15+40x+24)=

=(5x+3)²·(2x-1)³·(70x+9)