LISTA EXERCICIOS DE DERIVADAS COM RESPOSTA (06 de 13)

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Universidade de Mogi das Cruzes
6ª Lista de Exercícios de Cálculo I – A
 
Assunto: Diferenciação Profª Maria Helena Campanellli 
Exerc.s 181 a 183. Aplique a definição para achar a derivada da função.
181. f (x) = 3x²-5x –2 182. g (t) =
 183. h (s) = 
Exerc.s 184 e 185. Determine o coeficiente angular da reta tangente ao gráfico de f no ponto indicado.
184. f (x) = x³ + 3 ; P (-2 , -5) 185. f (x) = 
 + 1 ; P (4 , 3)
Exerc.s 186 e 187. Ache a equação da reta tangente ao gráfico de f no ponto indicado.
186. f ( x ) = 
 ; P (2, 2) 187. f ( x) = 
 ; P (1 , 1) 
Exerc.s 188 e 189. Ache o coeficiente angular e a equação da reta tangente ao gráfico 
no ponto (1 , 1) .
188. y = 
 189. y = 
Exerc.s 190 a 195. Indique os valores de x nos quais a função não é diferenciável. Explique por que ?
190. y = | x – 3 | 191. y = | x² - 9 | 192. y = 
193. y =
 194. y = 
 195. y = 
Exerc.s 196 a 220. Ache a derivada da função.
196. f (x) = 
 197. g (x) = 6
 + 2
198. f (s) = 
- 
 + 
 199. h (t) = 2
 + 
 - 
200. f (x) = 
 201. f (r) = 5 - 
+ 
202. g(x) = 
 203. h(x) = 
204. f (x) = 
 205. g (x) = 
206. h (t) =
 207. s (t) = 
 208. f(x) = 
+
 209. g (x) = 
 
210. h (t) = 
 211. f (t) = 
 
212. g (x) = (x² + 2).(x+ 1) 213. h (t) = (t² + 1)(1 - t³) 
214. f (x) = (2x + 1)(x - 1)(1 - x) 215. g (t) = 
216. f(t) = 
 217. f (x) = 
 218. h (t) = 
 219. f (x) = 
 220. f (x) = 
Respostas:
181. 6x –5 182. 
 183. 
 
184. 12 185. 
 186. y = 2x –2 
187. y = - x +2 188. 
 ; 
 189. –2 ; y = -2x + 3 
190. x = 3 (nó) 191. x= -3 e x = 3 (cúspide) 192. x = 1 
193. x = 3 (cúspide) 194. x= -1 (descontinuidade) 195. x = 0 (tangente vertical)
196. 
 197. 
 198. 
 
199. 
 200. 
 201. 
202. 
 203. 
 204. 24x.(3x²+1)³ 205. 
 206. 
 207. 
208. 
 209. 
 210. 
 
211. 
 212. 3x² + 2x + 2 213. 
 
214. 6x²- 6x 215. 
 216. (3t -1).(t + 2)³.(9t + 4) 
217. 
 218. 
 219. 
 
220. 
 
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