3.6-bo'lim : Ko'rsatkichli va logarifm funksiyalarning hosilalari
8. \(x = 2\) da \(f\left( x \right) = \ln \left( x \right){\log _2}\left( x \right)\) ga teguvchi chiziqni toping.
Yechim
Biz bilamizki, funktsiyaning hosilasi bizga teginish chizig'ining qiyaligini beradi, shuning uchun bizga funktsiyaning hosilasi kerak bo'ladi.
\[f'\left( x \right) = \frac{{{{\log }_2}\left( x \right)}}{x} + \frac{{\ln \left( x \right)}}{{x\ln \left( 2 \right)}}\]2-qadam
Endi biz qilishimiz kerak bo'lgan narsa bu funktsiyani va ko'rib chiqilayotgan nuqtadagi hosilani baholashdir.
\[f\left( 2 \right) = \ln \left( 2 \right){\log _2}\left( 2 \right) = \ln \left( 2 \right)\hspace{0.25in}\hspace{0.25in}f'\left( 2 \right) = \frac{{{{\log }_2}\left( 2 \right)}}{2} + \frac{{\ln \left( 2 \right)}}{{2\ln \left( 2 \right)}} = 1\]3-qadam
Endi biz qilishimiz kerak bo'lgan narsa teginish chizig'ining tenglamasini yozishdir.
\[y = f\left( 2 \right) + f'\left( 2 \right)\left( {x - 2} \right) = \ln \left( 2 \right) + \left( 1 \right)\left( {x - 2} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{x - 2 + \ln \left( 2 \right)}}\]