Question

Qual derivada de f(x) = 5( 2x elevado a 2 - 4x +2) elevado a 6

Answer 1

$\boxed{\boxed{f(x) = 5 ^{2x^2 -4x +2}}}$

pela tabela de derivada
$y = a ^u\\\\y' =a^u * ln(u) *u'$

temos
a = 5
u = 2x² -4x +2
u' = 4x - 4

$f'(x) = 5^{2x^2-4x+2} * ln(5)*(4x-4)\\\\f'(x) =5^{2*(x^2-2x+1)}* ln(5) * 4(x-1)\\\\\ f'(x) =25^{x^2-2x+1}*ln(5) * 4(x-1)\\\\ \boxed{\boxed{f'(x) = 25 ^{(x-1)^2} *4(x-1)* ln(5)}}$