3.10-bo'lim : Yashirin farqlash
10. \(\left( {1, - \sqrt 2 } \right)\) da \({x^4} + {y^2} = 3\) ga teguvchi chiziq tenglamasini toping.
Maslahat: Biz tangens chiziqlarning qiyaligini qanday hisoblashni bilamiz va bu nuqtada unchalik qiyin bo'lmasligi kerak bo'lgan aniq farqlash bilan.
Yechim
Birinchi narsa, bu funksiya uchun \(y'\) ni topish uchun yashirin farqlashdan foydalanishdir.
\[4{x^3} + 2y\,y' = 0\hspace{0.25in}\, \Rightarrow \hspace{0.25in}\,\,\,\underline {y' = - \frac{{2{x^3}}}{y}} \]2-qadam
Tangens chiziqning qiyaligini olish uchun ko'rib chiqilayotgan nuqtada hosilani baholash,
\[m = {\left. {y'} \right|_{x = 1,\,\,y = - \sqrt 2 }} = - \frac{2}{{ - \sqrt 2 }} = \sqrt 2 \]3-qadam
Endi biz faqat tangens chiziq tenglamasini yozishimiz kerak.
\[y - \left( { - \sqrt 2 } \right) = \sqrt 2 \left( {x - 1} \right)\hspace{0.25in}\, \Rightarrow \hspace{0.25in}\,\,\,\,y = \sqrt 2 \left( {x - 1} \right) - \sqrt 2 = \require{bbox} \bbox[2pt,border:1px solid black]{{\sqrt 2 \left( {x - 2} \right)}}\]