L7 LCC 14 2 Derivadas

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Universidade Federal da Para´ıba - UFPB
Centro de Cieˆncias Aplicadas e Educac¸a˜o - CCAE
Departamento de Cieˆncias Exatas - DCE
7a Lista de Exerc´ıcios - Ca´lculo I
Prof. Carlos Alberto Gomes de Almeida
1. Calcule f ′(x).
(a) f(x) = 3x2 + 5
(b) f(x) = 3x+
√
x
(c) f(x) = 2 3
√
x
(d) f(x) = 3
√
x+
√
x
(e) f(x) = 4x +
5
x2
(f) f(x) = 6x3 + 3
√
x
2. Calcule F ′(x) onde F(x) e´ igual a
(a)
x
x2 + 1
(b)
x2 − 1
x+ 1
(c)
3x2 + 3
5x− 3
(d)
√
x
x+ 1
(e)
√
x+
3
x3 + 2
(f)
3
√
x+ x√
x
(g) 5x+
x
x− 1
(h)
x+ 4
√
x√
x
(i) x3 +
x
5
√
x− 1
3. Calcule f ′(x) onde f(x) e´ igual a
(a) 3x2 + 5 cos(x)
(b)
cos(x)
x2 + 1
(c) x sin(x)
(d) x2 tan(x)
(e)
x+ 1
tan(x)
(f)
3
sin(x) + cos(x)
(g)
sec(x)
3x+ 2
(h) cos(x) + (x2 + 1) sin(x)
(i)
√
x sec(x)
(j) 3 cos(x) + 5 sec(x)
(k) x cot(x)
(l)
x+ 1
x sin(x)
(m)
x+ sin(x)
x− cos(x)
(n) (x3 +
√
x) csc(x)
4. Determine a derivada.
(a) y = sin(4x)
(b) f(x) = e3x
(c) f(x) = sin(t3)
(d) f(x) =
√
3x+ 1
(e) f(x) = cos(ex)
(f) f(x) = etan(x)
(g) f(t) = (t2 + 3)4
(h) y =
√
x+ ex
(i) y = cos(x2 + 3)
(j) y = ln(x2 + 3x+ 9)
5. Calcule a derivada.
(a) f(x) = 5x + log3 x
(b) f(x) = ln(3+ xx)
(c) f(x) = 32x+1 + log2(x
2 + 1)
(d) y = (3+ cos(x))x
(e) f(x) = xsin(3x)
(f) y = x(x
2+1)
(g) y = xx sin(x)
(h) y = xx
Bons estudos!!!
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