Páginas: 5 (1169 palavras) Publicado: 29 de maio de 2012

1) Calcule as seguintes derivadas usando a regra da potência, regra de uma soma, de um produto e do quociente:
a) f(x) = x5 R: 5x4
b) g(x) = x R: 1
c) h(x) = x10 R: 10x9
d) f(x) = 8x2 R: 16x
e)g(z) = -2z7 R: -14z6
f) f(x) = 3x4 + 8x + 15 R: 12x3 + 8
g) g(y) = 9y5 – 4y2 + 2y + 7 R: 45y4 - 8y + 2
h) f(x) = (2x3 – 1)(x4 + x2) R: 14x6 + 10x4 – 4x3 – 2x
i) f(t) = 1/2[(t2 + 5)(t6 + 4t)] R: 4t7 + 15t5 + 6t2 + 10
j) f(x) = 2x4 – 3 / x2 – 5x + 3 R: 4x5 – 30x4 + 24x3 + 6x – 15 / (x2 -5x + 3)2
k) f(x) = 1/x R: -1/x2

a) f(r) = πr2 R: 2πr
b) f(x) = 3x2 + 6x – 10 R: 6x + 6
c) f(w) = aw2 + b R: 2aw
d) f(x) = 14 – 1/2x-3 R: 3 / 2x4
e) f(x) = (2x + 1)(3x2 + 6) R: 18x2 + 6x + 12f) f(x) = (7x – 1)(x + 4) R: 14x + 27
g) f(x) = (3x5 – 1)(2 – x4) R: -27x8 + 30x4 + 4x3
h) f(x) = 2/3(5x – 3)-1(5x + 3) R: -20 / (5x – 3)2
i) f(x) = (x - 1)(x + 1) R: 2x
j) f(x) = 7(ax2 + bx + 6) R: 14ax + 7b
k) f(x) = (4x2 – a)(a – 2x) R: -24x2 + 8ax + 2a
l) f(x) = 2x + 4 / 3x – 1R: -14 / (3x – 1)2
m) f(t) = t – 1 / t + 1 R: 2 / (t + 1)2
n) f(t) = 3t2 + 5t – 1 / t – 1 R: 3t2 – 6t – 4 / (t – 1)2
o) f(t) = 2 – t2 / t – 2 R: - t2 + 4t – 2 / (t - 2)2
p) f(x) = 4 – x / 5 – x2 R: - x2 + 8x – 5 / (5 – x2)2
q) f(x) = 5x + 7 / 2x – 2 R: - 24 / (2x – 2)2r) f(x) = [x+1 / x+2](3x2 + 6x) R: 6x3 + 27x2 + 36x + 12/ (x + 2)2
s) f(t) = (t – a)2 / t – b R: t2 – 2bt + 2ab – a2 / (t - b)2
t) f(x) = (3/x4) + (5/x5) R: -12/x5 – 25/ x6
u) f(x) = (x4/2) + (2/x6) R: 2x3 – 12/x7

3) Calcule as seguintes derivadas; (exercícios de derivada de função composta ou regra da cadeia).a) y = x7 R: 7x6
b) y = x-7 R: -7/x8
c) y = (x2 + 1)7 R: 7(x2 + 1)6 ∙ 2x
d) y = (x2 – 5x +3)4 R : 4(x2 – 5x + 3)3 ∙ (2x – 5)
e) y = 1 / (x2 + 1)7 R : -14x / (x2 + 1)8
f) y = (3x + 2 / 2x + 1)5 R : -5(3x+ 2)4 / (2x + 1)6
g) y = (3x2 + 1)3∙(x – x2)2 R: 18x(3x2 + 1)2(x – x2)2 + (2(3x2 + 1)3(x – x2)(1 – 2x)

4) Derivar as seguintes funções;
a) f(t) = 12 – 3t4 + 4t6 R: - 12t3 + 24t5
b) g(x) = (x3 - 7)(x2 + 3) R: 2x4 + 9x2 + 28x
c) k(x) = (2x2 – 4x + 1)(6x - 5) R: 36x2 – 68x + 26
d) f(x) = 4x - 5 / 3x + 2R: 23 / 9x2 + 12x + 4
e) h(x) = 8x2 – 6x + 11 / x – 1 R: 8x2 – 16x - 5 / (x – 1)2
f) h(z) = 8 – z + 3z2 / 2 – 9z R: 70 + 12z – 27z2 / (2 – 9z)2
g) f(w) = 2w / x3 – 7 R: - 4w3 – 14 / (w3 – 7)2
h) f(x) = 3x3 - 2x2 + 4x – 7 R: 9x2 – 4x + 4
i) g(z) = 5z4 – 8z2 + z R: 20z3– 16z + 1
j) f(t) = t2 + 1/t2 R: 2t – 1/ 2t3
k) g(x) = (8x2 – 5x)(13x2 + 4) R: 416x3 – 195x2 + 64x - 20
l) h(y) = (y5 – 2y3)(7y2 + y - 8) R: 49y6 + 6y5 – 110y4 – 8y3 + 48y2
m) g(v) = v3 – 1 / v3 + 1 R: 6v2 / (v3 + 1)2
n) f(t) = 8t + 15 / t2 – 2t + 3 R: - 8t2 – 30t + 54...

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