Universidade Tecnológica Federal do Paraná - UTFPR

(a) Falsa
(b) Falsa
8. (a) y ′ = 4 cos 4x
(b) y ′ = −5 sin 5x
(c) y ′ = 3e 3x
(b) y ′ =
(e) y ′ = 3t 2 cos t 3
(f) g ′ (t) = 2
2t + 1
(g)
(h)
1(2 − x) 5
2 √ x + 1(x + 3) 7 − 5√ x + 1(2 − x) 4
(x + 3) 7 − 7√ x + 1(2 − x) 5
(x + 3) 8
x ′ = e sin t cos t
f ′ (x) = −e x sin e x
(i) y ′ = 3(sin x + cos x) 2 (cos x − sin x)
3
(j) y ′ =
2 √ 3x + 1
(k)
√ ( )
y ′ 2
x + 1 2
=
3(x + 1) 2 · 3
x − 1
(l)
y ′ = 2 tan(sin θ) sec 2 (sin θ) cos θ
(m) x ′ 2t + 3
=
t 2 + 3t + 9
(n)
f ′ (x) = e tan x sec 2 x
(o) y ′ = − sin x cos(cos x)
(p) g ′ (t) = 8t(t 2 + 3) 3
(q) f ′ (x) = −2x sin(x 2 + 3)
(r) y ′ = 1 + ex
2 √ x + e x
(s) y ′ = (ln(t4 ) + 4)
2 √ t ln(t 4 )
(t) y ′ = 3x2 cos(tan √ 1 + x 3 ) sec 2 √ 1 + x 3
(u) y ′ = e 3x (1 + 3x)
2 √ 1 + x 3
(v) y ′ = e x (cos 2x − 2 sin 2x)
(w) y ′ = e −x (cos x − sin x)
(x) y ′ = e −2t (3 cos 3t − 2 sin 3t)
(y) f ′ 2
(x) =
2x + 1 − 2xe−x2
(z) g ′ 4e 2t
(t) =
(e 2 t + 1) 2
(a 1 ) y ′ −5 sin 5x sin 2x − 2 cos 5x cos 2x
=
sin 2 2x
(b 1 ) f ′ (x) = 3(e −x + e x2 ) 2 (−e −x + 2xe x2 )
(c 1 ) y ′ = 3t 2 e −3t (1 − t)
(d 1 ) y ′ = 3(sin 3x + cos 2x) 2 (3 cos 3x − 2 sin 2x)
(e 1 ) y ′ 2x − e−x
=
2 √ x 2 + e −x
(f 1 ) y ′ 2x
= ln(2x + 1) +
(2x + 1)
(g 1 ) y ′ = 6x[ln(x2 + 1)] 2
(h 1 ) y ′ = sec x
x 2 + 1
(i 1 ) y ′ 2x + 8
=
x 2 + 8x + 1
(j 1 ) f ′ (x) =
3
√ 6x + 2
(k 1 ) f ′ (x) = e 3x x 3 (4 + 3x)
9. (a) y ′ = 1 − y4 − 2xy
4xy 3 + x 2 − 3
(c) Verdadeira
(d) Falsa
(l 1 ) f ′ (x) = 4 sin 3 x cos x
(m 1 ) f ′ (x) = 10 sec 2 2x
(n 1 ) f ′ (x) = (5 − x 2 ) 2 [(6x 2 − 3)(5 − x 2 ) − 6x(2x 3 − 3x)]
(o 1 ) f ′ 9
(x) =
2 √ (3x − 5) 3
(p 1 ) y ′ = e x2 +x+1 (2x + 1)
(q 1 ) y ′ = 2 cos 2x cos x − sin 2x sin x
(r 1 ) y ′ = 32(2x 2 − 4x + 1) 7 (x − 1)
(s 1 ) q ′ = 1 − r
√
2r − r 2
(t 1 ) s ′ = 3π 2 cos ( 3πx
2
)
− 3π 2
( ) 3πx
sin
2
(u 1 ) h ′ (x) = tan(2 √ x) + √ x sec 2 (2 √ x)
(v 1 ) r ′ = 2θ cos θ 2 cos 2θ − 2 sin θ 2 sin 2θ
(w 1 ) y ′ = (4x + 3)3 (4x + 7)
(x + 1) 4
(x 1 ) y ′ = e x sin e x − e cos x sin x
(y 1 ) y ′ = 5 sec 5x
(z 1 ) y ′ = −6x · cossec 2 (3x + 5)
(a 2 ) y ′ = (2e2x + e 3x )
(e x + 1) 2
(b 2 ) y ′ = 6x(x 4 − 3x 2 + 5) 2 (2x 2 − 3)
(c 2 ) y ′ = − sin(tan x) sec 2 x
(d 2 ) y ′ =
3x + 5
√ 2x + 1(2x + 1)
(e 2 ) y ′ = 2(2x2 + 1)
√
x 2 + 1
(f 2 ) y ′ = ex (1 + x 2 − 2x)
(1 + x 2 ) 2
(g 2 ) y ′ = 2e sin 2θ cos 2θ
(h 2 ) y ′ = e mx (m cos nx − n sin nx)
(i 2 ) y ′ = 1
2 √ x (cos √ x − √ x sin √ x)
(j 2 ) y ′ = cotan 4x − 4x · cossec 4x
(k 2 ) y ′ cos x − cos(x − sin x)
=
sin 2 (x − sin x)
(l 2 ) y ′ = −5cotan 5x
(m 2 ) y ′ 2 sec 2θ(tan 2θ − 1)
=
(1 + tan2θ) 2
(n 2 ) y ′ = e cx (c 2 sin x + sin x)
(o 2 ) y ′ = 2 + x
x
(p 2 ) y ′ = 2x sec(1 + x 2 ) tan(1 + x 2 )
(q 2 ) y ′ 1
= −
(x − 1) 2
(r 2 ) y ′ = − 1 2 √ x + 1
√
6
√ x
3
(x + √ x) 4
(s 2 ) y ′ = cos√ x
4 √ x sin √ x
(t 2 ) y ′ = (cotan x − sin x cos x) = cos3 x
(u 2 ) y ′ = − (x2 + 1) 3 (x 2 + 56x + 9)
(2x + 1) 4 (3x − 1) 6
(c) y ′ =
(2x − y cos xy)
x cos xy + 1
sin x
(b) y ′ =
y − 2x cos y
2 cos 2y − x 2 sin y − x
(d) y ′ =
ey
2 − xe y
6