Biz bilamizki, funktsiyaning hosilasi bizga teginish chizig'ining qiyaligini beradi, shuning uchun bizga funktsiyaning hosilasi kerak bo'ladi. Har bir atamani farqlash zanjir qoidasini ham talab qiladi.

\[\begin{align*}f\left( x \right) & = 4{\left( {2x} \right)^{\frac{1}{2}}} - 6{{\bf{e}}^{2 - x}}\\ f'\left( x \right) & = 4\left( {\frac{1}{2}} \right){\left( {2x} \right)^{ - \,\,\frac{1}{2}}}\left( 2 \right) - 6{{\bf{e}}^{2 - x}}\left( { - 1} \right) = 4{\left( {2x} \right)^{ - \,\,\frac{1}{2}}} + 6{{\bf{e}}^{2 - x}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{4}{{\sqrt {2x} }} + 6{{\bf{e}}^{2 - x}}}}\end{align*}\]

2-qadam

Endi biz qilishimiz kerak bo'lgan narsa bu funktsiyani va ko'rib chiqilayotgan nuqtadagi hosilani baholashdir.

\[f\left( 2 \right) = 4\left( 2 \right) - 6{{\bf{e}}^0} = 2\hspace{0.25in}\hspace{0.25in}f'\left( 2 \right) = \frac{4}{2} + 6{{\bf{e}}^0} = 8\]

3-qadam

Endi biz qilishimiz kerak bo'lgan narsa teginish chizig'ining tenglamasini yozishdir.

\[y = f\left( 2 \right) + f'\left( 2 \right)\left( {x - 2} \right) = 2 + 8\left( {x - 2} \right)\hspace{0.25in} \to \hspace{0.25in}\,\require{bbox} \bbox[2pt,border:1px solid black]{{y = 8x - 14}}\]