Taller Resuelto Deri y Opti
Enviado por jorshtv • 6 de Agosto de 2021 • Tareas • 1.301 Palabras (6 Páginas) • 55 Visitas
1.
𝐴 = 𝜋𝑟2
𝑑𝑟
𝑑𝑡 = 2 𝐼𝑛/𝑠𝑒𝑔[pic 1]
𝑑𝐴
𝑑𝑡 =? 𝑟 = 8𝑖𝑛[pic 2]
𝑑𝐴 𝑑𝑟
𝑑𝑡 = 𝜋2𝑟 ∗ 𝑑𝑡[pic 3][pic 4]
𝑑𝐴[pic 5]
𝑑𝑡
= 2 ∗ 𝜋 ∗ (8𝑖𝑛) ∗ (2 𝐼𝑛/𝑠𝑒𝑔 )
𝑑𝐴 = 32𝜋 = 100.530 𝐼𝑛2/𝑠𝑒𝑔[pic 6]
𝑑𝑡
2.
𝑑𝑣 = 9.5 𝐼𝑛3[pic 7]
𝑑𝑡
𝑑𝑟
𝑑𝑡 = 3 𝐼𝑛[pic 8]
𝑉 = 4 ∗ 𝜋𝑟3[pic 9]
3
𝑑𝑣 = 4 ∗ 𝜋 ∗ 3𝑟2 ∗ 𝑑𝑟[pic 10][pic 11][pic 12]
𝑑𝑡 3 𝑑𝑡
𝑑𝑟 = 4𝜋𝑟2 ∗ 𝑑𝑟[pic 13][pic 14]
𝑑𝑡
𝑑𝑟
= ([pic 15][pic 16]
𝑑𝑣
𝑑𝑡
𝑑𝑡
𝑑𝑟 9.5
) = =[pic 17][pic 18]
𝑑𝑡
4𝜋𝑟2
𝑑𝑡 4𝜋(3)2
𝑑𝑟 9.5
𝑑𝑡 = 36𝜋 𝐼𝑛/𝑚𝑖𝑛 = 0.0839 𝐼𝑛/𝑚𝑖𝑛[pic 19][pic 20]
3.
- Y= 3x2*secx
𝑦′ = 𝑑[pic 21]
𝑑𝑥
𝑦′ = 𝑑[pic 22]
𝑑𝑥
(3𝑥2 ∗ sec(𝑥))
(3𝑥2) ∗ sec(𝑥) + 3𝑥2 ∗ 𝑑[pic 23]
𝑑𝑥
(sec(𝑥))
𝑦′ = 3 ∗ 2𝑥 ∗ sec(𝑥) + 3𝑥2 + tan(𝑥) sec(𝑥)[pic 24]
𝑦′ = 3 ∗ 2𝑥 ∗ 1[pic 25][pic 26]
+ 3𝑥2 ∗ sin(𝑥) ∗ 1
𝑦′ =
6𝑥
[pic 27]
cos(𝑥)
cos(𝑥)
3𝑥2 ∗ sin(𝑥)
+ cos(𝑥)2[pic 28]
cos(𝑥)
cos(𝑥)
𝑦′ =[pic 29]
6𝑥 ∗ cos(𝑥) + 3𝑥2 ∗ sin(𝑥) cos(𝑥)2
- Y= 2x5 * cosx
𝑦′ = 𝑑[pic 30]
𝑑𝑥
𝑦′ = 𝑑[pic 31]
𝑑𝑥
(2𝑥5 ∗ cos(𝑥))
(2𝑥5) ∗ cos(𝑥) + 2𝑥5 ∗ 𝑑[pic 32]
𝑑𝑥
(cos(𝑥))
𝑦′ = 2 ∗ 5𝑥4 ∗ cos(𝑥) + 2𝑥5 ∗ (−sin(𝑥))
𝑦′ = 10𝑥4 ∗ cos(𝑥) − 2𝑥5 ∗ sin(𝑥)
c) Y= 3(2x4 + x3)5
𝑦′ = 3 ( 𝑑[pic 33]
𝑑𝑥
(2𝑥4 + 𝑥3)5)
𝑦′ = 3 ( 𝑑[pic 34]
𝑑𝑢
(𝑢5) ∗ 𝑑
𝑑𝑥[pic 35]
(2𝑥4 + 𝑥3))
𝑦′ = 3 (5𝑢4 ∗ 𝑑[pic 36]
𝑑𝑥
(2𝑥4 + 𝑥3))
𝑦′ = 3 (5(2𝑥4 + 𝑥3)4 ∗ 𝑑[pic 37]
𝑑𝑥
(2𝑥4 + 𝑥3))
𝑦′ = 15 ((2𝑥4 + 𝑥3)4 ∗ 𝑑[pic 38]
𝑑𝑥
(2𝑥4 + 𝑥3))
𝑦′ = 15(2𝑥4 + 𝑥3)4 ∗ ( 𝑑[pic 39]
𝑑𝑥
(2𝑥4) + 𝑑
𝑑𝑥[pic 40]
(𝑥3))
𝑦′ = 15(2𝑥4 + 𝑥3)4 ∗ (2 𝑑[pic 41]
𝑑𝑥
(𝑥4) + 𝑑
𝑑𝑥[pic 42]
(𝑥3))
𝑦′ = 15(2𝑥4 + 𝑥3)4 ∗ (2 𝑑[pic 43]
𝑑𝑥
(4𝑥3) + 𝑑
𝑑𝑥[pic 44]
(𝑥3))
𝑦′ = 15(2𝑥4 + 𝑥3)4 ∗ (8𝑥3 + 𝑑[pic 45]
𝑑𝑥
(𝑥3))
𝑦′ = 15(2𝑥4 + 𝑥3)4 ∗ (8𝑥3 + 3𝑥2)
[pic 46]
Y= √1−𝑥2
(𝑥+1)3[pic 47][pic 48][pic 49][pic 50]
1
(1−𝑥2)2
[pic 51]
2
(𝑥+1)3[pic 52]
...