sin的平方2x求导等于多少 sin^2x的导数是多少?

sin^2x\u7684\u5bfc\u6570\u662f\u591a\u5c11\uff1f

sin²x

=(sinx)²

=2sinx(sinx)'

=2sinxcosx

=sin2x
\u51fd\u6570\u53ef\u5bfc\u7684\u6761\u4ef6\uff1a

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\u53ef\u5bfc\u7684\u51fd\u6570\u4e00\u5b9a\u8fde\u7eed\uff1b\u8fde\u7eed\u7684\u51fd\u6570\u4e0d\u4e00\u5b9a\u53ef\u5bfc\uff0c\u4e0d\u8fde\u7eed\u7684\u51fd\u6570\u4e00\u5b9a\u4e0d\u53ef\u5bfc\u3002

\u6839\u636e\u590d\u5408\u51fd\u6570\u7684\u6c42\u5bfc\u6cd5\u5219\uff1a
sin²x
=(sinx)²
=2sinx(sinx)'
=2sinxcosx
=sin2x

y=(sin2x)^2
y'
=2(sin2x).(sin2x)'
=2(sin2x).(cos2x).(2x)'
=2(sin2x).(cos2x).(2)
=4(sin2x).(cos2x)

sin鐨勫钩鏂2x姹傚绛変簬澶氬皯
绛旓細=2(sin2x).(cos2x).(2)=4(sin2x).(cos2x)

sin²2x姹傚绛変簬浠涔?
绛旓細4sin4x

sin^2x姹傚绛変簬澶氬皯?
绛旓細d{ [sin(x)]^2 }/dx = 2sin(x)*cos(x) = sin(2x)

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绛旓細sin骞虫柟x鐨勫鏁鍙互鍐欐垚锛氾紙sin²x锛'=2sinx锛坰inx锛'=2sinxcosx=sin2x銆俿inx骞虫柟锛歽=sinx^2锛寉'=cosx^2*2x=2xcosx^2 瀵兼暟鏄鍑芥暟鍥惧儚鍦ㄦ煇涓鐐瑰鐨勬枩鐜囷紝涔熷氨鏄旱鍧愭爣澧為噺锛埼攜锛夊拰妯潗鏍囧閲忥紙螖x锛夊湪螖x-->0鏃剁殑姣斿笺傚井鍒嗘槸鎸囧嚱鏁板浘鍍忓湪鏌愪竴鐐瑰鐨勫垏绾垮湪妯潗鏍囧彇寰楀閲徫攛浠ュ悗锛...

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绛旓細杩愮畻鏂规硶鏈変互涓嬩袱绉嶏細1.(sin²x)'=2sinx(sinx)'=2sinxcosx=sin2x銆2.(sin²x)'=[(1-cos2x)/2]'=[1/2-(cos2x)/2]'=0-½(-sin2x)(2x)'=½(sin2x)脳2=sin2x銆瀵兼暟绗竴瀹氫箟 璁惧嚱鏁皔=f(x)鍦ㄧ偣x0鐨勬煇涓偦鍩熷唴鏈夊畾涔夊綋鑷彉閲弜鍦▁0澶勬湁澧為噺鈻硏(x0+...

sin²x姹傚,sin2x姹傚,sinx²姹傚
绛旓細sin²x=(sinx)²锛(sin²x)' = 2sinx路(sinx)'=2sinxcosx=sin2x (sin2x)' =(cos2x)脳2=2cos2x (sinx²)'=cosx² 路 (x²)' = 2xcosx²

sinx骞虫柟鐨勫鏁鎬庝箞绠楃殑
绛旓細(sin²x)'= [(1-cos2x)/2]'= [1/2 - (cos2x)/2]'= 0 - ½(-sin2x)(2x)'= ½(sin2x)脳2 = sin2x 鈭玡^(kx) dx = (1/k)e^(kx) + C 鎵浠モ埆e^(5x) dx =(1/5)鈭玡^(5x) d(5x) =(1/5)e^(5x) + C 鍜岃鍏紡锛歴in ( 伪 卤 尾 ) = ...

sin^2x姹傚绛変簬澶氬皯?姹傝繃绋
绛旓細锛sin^2x锛夆=cos2x*(2x)'=2cos2x

sin骞虫柟x鐨勫鏁
绛旓細杩愮畻鏂规硶鏈変互涓嬩袱绉嶏細1.(sin²x)' = 2sinx(sinx)' = 2sinxcosx = sin2x銆2.(sin²x)' = [(1-cos2x)/2]' = [1/2 - (cos2x)/2]' = 0 - ½(-sin2x)(2x)' = ½(sin2x)脳2 = sin2x銆

y=sin(x²)鐨勫鏁?
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細鑻ユ湁甯姪锛岃閲囩撼銆

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