13.6-bo'lim : Zanjir qoidasi
9. Quyidagi tenglama uchun \(\displaystyle \frac{{dy}}{{dx}}\) ni hisoblang.
\[{x^2}{y^4} - 3 = \sin \left( {xy} \right)\]Yechim
Avval tenglamani tezda qayta yozing.
\[{x^2}{y^4} - 3 - \sin \left( {xy} \right) = 0\]2-qadam
Oldingi bosqichdagi qayta yozishdan shuni ko'rishimiz mumkinki,
\[F\left( {x,y} \right) = {x^2}{y^4} - 3 - \sin \left( {xy} \right)\]Endi biz hosila olish uchun eslatmalarda olingan formuladan foydalanishimiz mumkin.
\[\frac{{dy}}{{dx}} = - \frac{{{F_x}}}{{{F_y}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{ - \frac{{2x{y^4} - y\cos \left( {xy} \right)}}{{4{x^2}{y^3} - x\cos \left( {xy} \right)}} = \frac{{y\cos \left( {xy} \right) - 2x{y^4}}}{{4{x^2}{y^3} - x\cos \left( {xy} \right)}}}}\]E'tibor bering, javobning ikkinchi shaklida biz kasr oldidagi "-" belgisini suratga ko'chirdik va uni ko'paytirdik. Agar xohlasak, biz buni maxraj yordamida osonlikcha bajarishimiz mumkin edi.