𝑑𝑦
𝑦 ′ = 𝑑𝑥
sin(𝑥 2 + 𝑦) = 𝑦 −2 + 𝑥 3
sin(𝑥 2 + 𝑦) = 𝑦 −2 + 𝑥 3
𝑑𝑦
𝑑𝑦
cos(𝑥 2 + 𝑦) ∙ (2𝑥 + ) = −2𝑦 −3
+ 3𝑥 2
𝑑𝑥
𝑑𝑥
𝑑𝑦
𝑑𝑦
2
2
2𝑥 cos(𝑥 + 𝑦) + cos(𝑥 + 𝑦)
= −2𝑦 −3
+ 3𝑥 2
𝑑𝑥
𝑑𝑥
𝑑𝑦
𝑑𝑦
2
−3
2
cos(𝑥 + 𝑦)
+ 2𝑦
= 3𝑥 − 2𝑥 cos(𝑥 2 + 𝑦)
𝑑𝑥
𝑑𝑥
𝑑𝑦
(cos(𝑥 2 + 𝑦) + 2𝑦 −3 )
= 3𝑥 2 − 2𝑥 cos(𝑥 2 + 𝑦)
𝑑𝑥
𝑑𝑦 3𝑥 2 − 2𝑥 cos(𝑥 2 + 𝑦)
=
𝑑𝑥
cos(𝑥 2 + 𝑦) + 2𝑦 −3
𝒅𝒚 𝟑𝒙𝟐 − 𝟐𝒙 𝐜𝐨𝐬(𝒙𝟐 + 𝒚)
=
𝒅𝒙
𝐜𝐨𝐬(𝒙𝟐 + 𝒚) + 𝟐𝒚−𝟑
1
4
25
𝑦
𝑥
𝑑𝑥
1
= − 𝑓𝑡/𝑠𝑒𝑐
𝑑𝑡
4
𝑑𝑦
=?
𝑑𝑡
𝑡 = 12 𝑠𝑒𝑐
1
→ 𝑥 = 10 − (12) = 10 − 3 = 7
4
2
√
→ 𝑦 = 25 − 72 = 24
𝑥 2 + 𝑦 2 = 252
𝑑𝑥
𝑑𝑦
2𝑥
+ 2𝑦
=0
𝑑𝑡
𝑑𝑡
1
𝑑𝑦
2(7) (− ) + 2(24)
=0
4
𝑑𝑡
1
𝑑𝑦
2(7) (− ) + 2(24)
=0
4
𝑑𝑡
𝑑𝑦
7
=
≈ 0.073 𝑓𝑡/𝑠𝑒𝑐
𝑑𝑡 96
𝟕
𝟗𝟔
𝒇𝒕/𝒔𝒆𝒄