Calculo I exercícios de derivadas

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LISTA DE EXERCÍCIOS PROPOSTOS PARA A REVISÃO DOS CONCEITOS
	Exercício: DERIVE
	RESPOSTA
	y = sen 4x
	4 cos 4x
	y = cos 5x
	–5 sen 5x
	y = e3x
	3e3x
	f(x) = cos 8x
	–8 sen 8x
	y =sen t3
	3t2 cos t3
	g(t) = ln (2t+1)
	
	x = esen t
	e sen t cos t
	f(x) = 
	–ex sen ex
	y = (sen x + cos x)3
	3(sen x + cos x)2 (cos x – sen x)
	
	
	
	
	y = e-5x
	–5e-5x
	x = ln (t2 +3t+9)
	
	f(x) = etg x
	etg x sec2 x
	y = sen(cosx)
	–sen x cos (cos x)
	g(t) = (t2+3)4
	8t (t2 + 3)3
	f(x) = cos(x2 + 3)
	–2x sen (x2 + 3)
	 
	
	y = tg 3x
	3 sec2 3x
	y = sec 3x
	3 sec 3x tg 3x
	y = xe3x
	21. e3x (1+3x)
	y = ex . cos 2x
	22. ex (cos 2x – 2 sen 2x) 
	23. y = e-x sen x 
	23. e-x (cos x – sen x)
	24. y = e-2t sen 3t
	24. e-2t (3 cos 3t – 2 sen 3t)
	25. f(x) = 
+ ln (2x + 1)
	25. 
	26. 
	26. 
	27. 
	27. 
	28. f(x) = 
	28. 
	29. y = t3 e-3t
	29. 3t2 e-3t(1 – t)
	30. y = (sen 3x + cos 2x)3 
	30. 3(sen 3x + cos 2x)2 (3 cos 3x – 2 sen 2x)
	31.
	31. 
	32. y = x ln (2x + 1)
	32. 
	33. y = [ln (x2 + 1)]3
	33. 
	34. y = ln (sec x + tg x)
	34. sec x
LISTA DE EXERCÍCIOS DE REVISÃO DOS CONCEITOS DE DERIVADAS
Calcule as derivadas:
f(x) = 16x3 – 4x2 + 3
f(x) = (x2 + 3x + 3) . (x + 3)
f(x) = ln (x2 + 8x + 1)
f(x) = x4 . e3x
f(x) = sen4 x
f(x) = 5 tg 2x
Derive as seguintes funções:
f(x) = - 5x3 + 21x2 – 3x + 4
f(x) = (2x3 – 3x) (5 – x2)3
Determine a derivada das seguintes funções:
 
y = sen 2x . cos x 
y = (2x2 - 4x +1 )8
 
Usando as regras de derivação, calcule a derivada das funções abaixo:
				b) 
Usando a definição (de derivadas) 
, calcule a derivada das seguintes funções nos pontos dados:
a) f(x) = 2x2 – 3x + 4 ; P0 = (2, 6)
b) 
c) 
d) 
e) 
Usando as regras de derivação, calcule a derivada (função derivada) das funções abaixo:
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