Universidade Tecnológica Federal do Paraná - UTFPR

Respostas
1. (a) f ′ (2) = 5
(b) f ′ (1) = −6
(c) f ′ (8) = 1
(
12
π
)
(d) g ′ = −1
2
2. (a) f ′ (x) = 48x 2 − 8x
(b) f ′ (x) = −15x 2 + 42x − 3
(c) f ′ (x) = 0
(d) f ′ (x) = 2
(e) y ′ = 0
(f) y ′ = 2
(g) y ′ = 2
5 5√ x 3 − 3
4 4√ x + 4x3
(h) f ′ (x) = 4
5 5√ x − 1
6 6√ x 5
(i) f ′ (x) = 0
(j) s ′ (t) =
−33
(2t − 7) 2
(k) f ′ (x) = − 3 x + √ 1 + 1
2 x 8x √ x
(l) f ′ −8r − 15
(r) =
r 4
(m) f ′ (x) = 2(−6x 2 + 2x + 1)
(e) f ′ (2π) = 3
(f) v ′ (4) = − 11
16
(g) f ′ (−3) = 11 e f ′ (0) = 5
(h) f ′ (−3) = 0
(n) y ′ = x(−27x 7 + 7x 5 + 12x 2 − 2)
(o) g ′ (t) = 7 − 5t2 + 4t
(1 + t + t 2 ) 2
(p) f ′ (x) = x 2 + 4x + 4
(q) f ′ (x) = x2 (4x + 3)
(2x + 1) 2
(r) y ′ = 3x 5 + 5x 4 − 6x − 6
(s) g ′ (x) = x2 + x + 4
(x + 0, 5) 2
(t) r ′ = 1 √
θ
− 1
θ √ θ
(u) f ′ (x) =
(v) v ′ = t2 − 2t − 1
(1 + t 2 ) 2
−4x 3 − 3x 2 + 1
((x 2 − 1)(x 2 + x + 1)) 2
(w) y ′ = 1
2 √ x − 4
3x 2 3√ x
3. (a) f ′ (x) = sec 2 x
(b) g ′ (t) = tan t · sec t
(c) f ′ (x) =
2 sin x + x2
2 √ x
(e)
(d) h ′ (θ) = π cos θ + sin θ
2
+ 2 √ x(cos x + x)
y ′ = 3x 2 + 1 2 sin x
(f) y ′ = − 15
8x 4 + 2 cos x
(g) y ′ = 5 cos x − 3 x 2
(h) y ′ 1
= −
2 sin x cos x + 1
4. (a) f ′ (x) = ex (sin x + cos x)
(f) y ′ = e x · x
cos 2 x
(b) f ′ (x) = e x (sin x + cos x)
(g) y ′ = e x (x 2 + x − 1)
(c) f ′ (x) = x(2 ln x + 1)
(d) f ′ (x) = e x (x 2 (h) y ′ = 2e x
+ 2x + 1)
(e) y ′ e x
=
(2e x + 1) 2 (i) y ′ = (−t2 + 4t − 4)
e t
5. (a) y ′ (1) = 7 16
(b) y ′ (1) = − 13
8
6. Verdadeira
4
(c) y ′ (1) = −29
(d) Descontínua em x = 1