cho ham so y= √e √e √e √e √x ,(x>0) tim dao ham cua y giup mink voi 29/07/2021 Bởi Samantha cho ham so y= √e √e √e √e √x ,(x>0) tim dao ham cua y giup mink voi
Đáp án: $y’=\dfrac{1}{4}e^\tfrac{15}{16}.x^\tfrac{-3}{4}$ Giải thích các bước giải: $y=\sqrt{e\sqrt{e\sqrt{e\sqrt{e\sqrt{x}}}}}\\ =\left(e\left(e\left(e\left(e\sqrt{x}\right)^\tfrac{1}{2}\right)^\tfrac{1}{2}\right)^\tfrac{1}{2}\right)^\tfrac{1}{2}\\ =e^\tfrac{1}{2}.e^\tfrac{1}{4}.e^\tfrac{1}{8}.e^\tfrac{1}{16}.x^\tfrac{1}{32}\\ =e^\tfrac{15}{16}.x^\tfrac{1}{32}\\ y’=\dfrac{1}{32}e^\tfrac{15}{16}.x^\tfrac{-31}{32}$ Bình luận
Đáp án:
$y’=\dfrac{1}{4}e^\tfrac{15}{16}.x^\tfrac{-3}{4}$
Giải thích các bước giải:
$y=\sqrt{e\sqrt{e\sqrt{e\sqrt{e\sqrt{x}}}}}\\ =\left(e\left(e\left(e\left(e\sqrt{x}\right)^\tfrac{1}{2}\right)^\tfrac{1}{2}\right)^\tfrac{1}{2}\right)^\tfrac{1}{2}\\ =e^\tfrac{1}{2}.e^\tfrac{1}{4}.e^\tfrac{1}{8}.e^\tfrac{1}{16}.x^\tfrac{1}{32}\\ =e^\tfrac{15}{16}.x^\tfrac{1}{32}\\ y’=\dfrac{1}{32}e^\tfrac{15}{16}.x^\tfrac{-31}{32}$