(Até 4 pontos)
e) e^(x^3)

Passo 1

Beleza, vamos começar! O enunciado pede para trabalharmos com a função . Isso está relacionado ao cálculo de derivadas, mais especificamente usando a Regra da Cadeia. Para resolver, vamos precisar conhecer como derivar funções exponenciais e como aplicar a Regra da Cadeia quando temos uma função composta.

Passo 2

Primeiro, vamos relembrar que a derivada de , onde é uma função de , é vezes a derivada de . Ou seja:

Passo 3

No nosso caso, . Então, vamos calcular a derivada de em relação a :

Passo 4

Agora, aplicando a Regra da Cadeia, substituímos e na fórmula da derivada de :

Resposta

A derivada de é .

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(Até 4 pontos)
c) 7
<html><head></head><body><div>(Até 4 pontos)<br>
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(Até 4 pontos)
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