calculo dif

2.
𝑦 = 3𝑥(𝑥 2 − 𝑥 + 1) ∙ (5𝑥 − 3)
𝑦 = (3𝑥 3 − 3𝑥 2 + 3𝑥) ∙ (5𝑥 − 3)
𝑦 = 15𝑥 4 − 24𝑥 3 + 24𝑥 2 − 9𝑥
𝑦 ′ = 4(15𝑥 3 ) − 3(24𝑥 2 ) + 2(24𝑥) − 9
𝑦 = (𝑥 + 5) ∙ (𝑥 3 − 1) ∙ (𝑥 2 − 𝑥 + 3)
𝑦 = (𝑥 4 + 5𝑥 3 − 𝑥 − 5) ∙ (𝑥 2 − 𝑥 + 3)
𝑦 = 𝑥 6 + 4𝑥 5 − 2𝑥 4 + 14𝑥 3 − 4𝑥 2 + 2𝑥 − 15
𝑦 ′ = 6𝑥 5 + 5(4𝑥 4 ) − 4(2𝑥 3 ) + 3(14𝑥 2 ) − 2(4𝑥) + 2
12.
𝑦 = 𝑎3𝑥+5 ∙ (𝑥 2 − 𝑥 + 1)
𝑦 ′ = (𝑎3𝑥+5 ∙ 3 ∙ 𝑙𝑛𝑎)(𝑥 2 − 𝑥 + 1) + (𝑎3𝑥+5 )(2𝑥 − 1)
𝑦 = 5𝑥+3
𝑦 ′ = (5𝑥+3 )𝑙𝑛5 ∙ 1
7.
𝑦 = √𝑥 2 + 5𝑥 − 4
𝑦′ =
1
2(√𝑥 2
+ 5𝑥 − 4
∙ (2𝑥 + 5)
3
𝑦 = √𝑥 2 − 5𝑥
1
𝑦′ =
3(𝑥 2
2
− 5𝑥)3
∙ (2𝑥 − 5)
13.
𝑦 = ln (𝑥 + √𝑥 2 + 9)
𝑦′ =
𝑦′ =
𝑦′ =
1
∙ (1 +
𝑥 + √𝑥 2 + 9
1
𝑥 + √𝑥 2 + 9
1
2√𝑥 2 + 9
∙ 2𝑥)
𝑥
+
(𝑥 + √𝑥 2 + 9)(√𝑥 2 + 9)
(𝑥 + √𝑥 2 + 9)(√𝑥 2 + 9) + 𝑥(𝑥 + √𝑥 2 + 9)
(𝑥 + √𝑥 2 + 9)2 (√𝑥 2 + 9)
𝑦′ =
√𝑥 2 + 9 + 𝑥
(𝑥 + √𝑥 2 + 9)(√𝑥 2 + 9)
𝑦′ =
1
√𝑥 2
+9
3.
𝑦=
𝑦′ =
𝑥 2 − 3𝑥 + 4
3𝑥 − 4
(2𝑥 − 3)(3𝑥 − 4) − (𝑥 2 − 3𝑥 + 4)(3)
(3𝑥 − 4)2
𝑦′ =
3𝑥 2 − 8𝑥
(3𝑥 − 4)2
3𝑥 2 − 6
𝑦= 2
𝑥 +𝑥+1
𝑦′ =
(6𝑥)(𝑥 2 + 𝑥 + 1) − (3𝑥 2 − 6)(2𝑥 + 1)
(𝑥 2 + 𝑥 + 1)2
3𝑥 2 + 18𝑥 + 6
𝑦 = 2
(𝑥 + 𝑥 + 1)2
′
8.
4
𝑦 = √𝑥 3 − 𝑥 + 3
𝑦′ =
1
∗
4
1
(𝑥 3
−𝑥+
3
3)4
∗ 3𝑥 2 − 1
3𝑥 2 − 1
𝑦′ =
3
4(𝑥 3 − 𝑥 + 3)4
3
𝑦 = √(𝑥 3 + 𝑥 2 − 7)
𝑦′ =
1
∗
3
1
(𝑥 3
𝑦′ =
+
𝑥2
2
− 7)3
∗ (3𝑥 2 + 2𝑥)
(3𝑥 2 + 2𝑥)
2
3(𝑥 3 + 𝑥 2 − 7)3