Question

Nos exercícios abaixo calcular as derivadas sucessivas até a ordem n indicada y = 3x4 – 2x; n = 5

Answer 1

y=3$x^{4}$-2x

y'=12$x^{3}$ -2

y''=36$x^{2}$

y'''=72x

y''''=72

y'''''=0

Answer 2

$Fun\c{c}\~ao:\\\\ y=3x^4-2x\\\\\\ Calculando\ a\ derivada\ n=1:\\\\ y'=3(4)x^{4-1}-2(1)x^{1-1}\\\\ y'=12x^{3}-2\\\\\\ Calculando\ a\ derivada\ n=2:\\\\ y''=12(3)x^{3-1}-\not2\\\\ y''=36x^{2}$



$Calculando\ a\ derivada\ n=3:\\\\ y'''=36(2)x^{2-1}\\\\ y'''=72x\\\\\\ Calculando\ a\ derivada\ n=4:\\\\ y''''=72(1)x^{1-1}\\\\ y''''=72\\\\\\ Calculando\ a\ derivada\ n=5:\\\\ y'''''=\not7\not2\ (derivada\ de\ constante\ \'e\ zero)\\\\ \boxed{y'''''=0}$


Espero ter ajudado.
Bons estudos!