Найти производную f(x)=4x^4*√x​

18х³√х

Объяснение:

f(x)=4x⁴•√x

f'(x) = (4x⁴•√x)' = 4 • (x⁴•√x) =

= 4 • ( (x⁴)'•√x + x⁴•(√x)' ) =

= 4 • ( 4х³•√x + x⁴•1 / (2•√х) )=

= 4 • ( 4х³√х + 0,5х³√х ) =

= 4 • 4,5 х³√х =

= 18х³√х

f(x)=4x⁴√x = 4 • x⁴ • x^(1/2) =

= 4 • x^ (4+1/2) = 4 • x^(4,5)

f'(x) = ( 4 • x^(4,5) )' = 4 ( x^(4,5) )' =

= 4 • 4,5 • x^(4,5-1) = 4•4,5•x^(3,5)=

=18•x^(3+0,5)=18•x^(3)•x^(0,5)=18x³√x