cho ham so y= √e √e √e √e √x ,(x>0) tim dao ham cua y giup mink voi

0 bình luận về “cho ham so y= √e √e √e √e √x ,(x>0) tim dao ham cua y giup mink voi”

1. Đáp án:

   $y’=\dfrac{1}{4}e^\tfrac{15}{16}.x^\tfrac{-3}{4}$

   Giải thích các bước giải:

   $y=\sqrt{e\sqrt{e\sqrt{e\sqrt{e\sqrt{x}}}}}\\ =\left(e\left(e\left(e\left(e\sqrt{x}\right)^\tfrac{1}{2}\right)^\tfrac{1}{2}\right)^\tfrac{1}{2}\right)^\tfrac{1}{2}\\ =e^\tfrac{1}{2}.e^\tfrac{1}{4}.e^\tfrac{1}{8}.e^\tfrac{1}{16}.x^\tfrac{1}{32}\\ =e^\tfrac{15}{16}.x^\tfrac{1}{32}\\ y’=\dfrac{1}{32}e^\tfrac{15}{16}.x^\tfrac{-31}{32}$

   Trả lời