3.10-bo'lim: Yashirin farqlash
1-3-muammolar uchun quyidagi amallarning har birini bajaring.
- Y uchun tenglamani yechish va to'g'ridan-to'g'ri differentsiallash orqali \(y'\) ni toping.
- Yashirin farqlash orqali \(y'\) ni toping.
- (a) va (b) dagi hosilalar bir xil ekanligini tekshiring.
- \(\displaystyle \frac{x}{{{y^3}}} = 1\) Yechim
- \({x^2} + {y^3} = 4\) Yechim
- \({x^2} + {y^2} = 2\) Yechim
4-9-masalalar uchun aniq farqlash orqali \(y'\) ni toping.
- \(2{y^3} + 4{x^2} - y = {x^6}\) Yechim
- \(7{y^2} + \sin \left( {3x} \right) = 12 - {y^4}\) Yechim
- \({{\bf{e}}^x} - \sin \left( y \right) = x\) Yechim
- \(4{x^2}{y^7} - 2x = {x^5} + 4{y^3}\) Yechim
- \(\cos \left( {{x^2} + 2y} \right) + x\,{{\bf{e}}^{{y^{\,2}}}} = 1\) Yechim
- \(\tan \left( {{x^2}{y^4}} \right) = 3x + {y^2}\) Yechim
10 va 11-masalalar uchun berilgan nuqtadagi tangens chiziq tenglamasini toping.
- \({x^4} + {y^2} = 3\) at \(\left( {1,\, - \sqrt 2 } \right)\). Yechim
- \({y^2}{{\bf{e}}^{2x}} = 3y + {x^2}\) at \(\left( {0,3} \right)\). Yechim
12 va 13-masalalar uchun \(x = x\left( t \right)\), \(y = y\left( t \right)\) va \(z = z\left( t \right)\) keyin berilgan tenglamani t ga nisbatan differensiallashini faraz qiling.