حمّل تطبيق منهاجي الجديد

منهاجي صار أسرع من خلال التطبيق

  أتحقق من فهمي

أتحقق من فهمي

مشتقتا اقتران الجيب واقتران جيب التمام

مشتقة اقتران الجيب، ومشتقة اقتران جيب التمام

أتحقق من فهمي صفحة 83

أجد مشتقة كل اقتران ممّا يأتي:

(a) begin mathsize 20px style f left parenthesis x right parenthesis equals 7 plus sin invisible function application space x end style

begin mathsize 20px style f to the power of straight prime left parenthesis x right parenthesis equals c o s invisible function application space x end style

(b) begin mathsize 20px style f left parenthesis x right parenthesis equals 3 x minus cos invisible function application space x end style

begin mathsize 20px style f to the power of straight prime left parenthesis x right parenthesis equals 3 plus s i n invisible function application space x end style

(c) begin mathsize 20px style f left parenthesis x right parenthesis equals 3 sin invisible function application space x plus 2 cos invisible function application space x end style

begin mathsize 20px style f to the power of straight prime left parenthesis x right parenthesis equals 3 c o s invisible function application space x minus 2 s i n invisible function application space x end style

 

مشتقتا الضرب والقسمة المتضمنتان اقتراني الجيب وجيب التمام

أتحقق من فهمي صفحة 84

أجد مشتقة كل اقتران ممّا يأتي:

(a) begin mathsize 20px style f left parenthesis x right parenthesis equals e to the power of x space cos invisible function application space x end style

begin mathsize 20px style f to the power of straight prime left parenthesis x right parenthesis equals left parenthesis e to the power of x right parenthesis left parenthesis negative s i n invisible function application space x right parenthesis plus left parenthesis c o s invisible function application space x right parenthesis left parenthesis e to the power of x right parenthesis equals negative e to the power of x s i n invisible function application space x plus e to the power of x space c o s invisible function application space x end style

(b) begin mathsize 20px style f left parenthesis x right parenthesis equals fraction numerator x plus cos invisible function application space x over denominator sin invisible function application space x end fraction end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell f to the power of straight prime left parenthesis x right parenthesis end cell cell equals fraction numerator left parenthesis s i n invisible function application space x right parenthesis left parenthesis 1 minus s i n invisible function application space x right parenthesis minus left parenthesis x plus c o s invisible function application space x right parenthesis left parenthesis c o s invisible function application space x right parenthesis over denominator s i n squared invisible function application space x end fraction end cell row blank cell equals fraction numerator s i n invisible function application space x minus s i n squared invisible function application space x minus x c o s invisible function application space x minus c o s squared invisible function application space x over denominator s i n squared invisible function application space x end fraction end cell row blank cell equals fraction numerator s i n invisible function application x minus left parenthesis s i n squared invisible function application space x plus c o s squared invisible function application space x right parenthesis minus x c o s invisible function application space x over denominator s i n squared invisible function application space x end fraction end cell row blank cell equals fraction numerator s i n invisible function application space x minus 1 minus x c o s invisible function application space x over denominator s i n squared invisible function application space x end fraction end cell end table end style

 

مشتقتا اقتران الجيب واقتران جيب التمام، وقاعدة السلسلة

أتحقق من فهمي صفحة 86

(a) begin mathsize 20px style f left parenthesis x right parenthesis equals cos invisible function application space 5 x end style

begin mathsize 20px style f to the power of straight prime left parenthesis x right parenthesis equals negative 5 s i n invisible function application space 5 x end style

(b) begin mathsize 20px style f left parenthesis x right parenthesis equals square root of sin invisible function application space x end root end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell E left parenthesis x right parenthesis equals sum x p left parenthesis x right parenthesis equals 0 left parenthesis 1 fourth right parenthesis plus 1 left parenthesis 3 over 8 right parenthesis plus 2 left parenthesis 1 over 8 right parenthesis plus 3 left parenthesis 1 fourth right parenthesis equals 3 over 8 plus 2 over 8 plus 6 over 8 equals 11 over 8 end cell row blank cell sigma squared equals E left parenthesis x squared right parenthesis minus left parenthesis E left parenthesis x right parenthesis right parenthesis squared equals 0 squared left parenthesis 1 fourth right parenthesis plus 1 squared left parenthesis 3 over 8 right parenthesis plus 2 squared left parenthesis 1 over 8 right parenthesis plus 3 squared left parenthesis 1 fourth right parenthesis minus left parenthesis 11 over 8 right parenthesis squared end cell row blank cell equals 0 plus 3 over 8 plus 4 over 8 plus 9 over 8 minus 121 over 64 equals 16 over 8 minus 121 over 64 equals 7 over 64 end cell row blank blank end table end style

(c) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell E left parenthesis x right parenthesis equals sum x p left parenthesis x right parenthesis equals 0 left parenthesis 1 fourth right parenthesis plus 1 left parenthesis 3 over 8 right parenthesis plus 2 left parenthesis 1 over 8 right parenthesis plus 3 left parenthesis 1 fourth right parenthesis equals 3 over 8 plus 2 over 8 plus 6 over 8 equals 11 over 8 end cell row blank cell sigma squared equals E left parenthesis x squared right parenthesis minus left parenthesis E left parenthesis x right parenthesis right parenthesis squared equals 0 squared left parenthesis 1 fourth right parenthesis plus 1 squared left parenthesis 3 over 8 right parenthesis plus 2 squared left parenthesis 1 over 8 right parenthesis plus 3 squared left parenthesis 1 fourth right parenthesis minus left parenthesis 11 over 8 right parenthesis squared end cell row blank cell equals 0 plus 3 over 8 plus 4 over 8 plus 9 over 8 minus 121 over 64 equals 16 over 8 minus 121 over 64 equals 7 over 64 end cell row blank blank end table end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell E left parenthesis x right parenthesis equals sum x p left parenthesis x right parenthesis equals 0 left parenthesis 1 fourth right parenthesis plus 1 left parenthesis 3 over 8 right parenthesis plus 2 left parenthesis 1 over 8 right parenthesis plus 3 left parenthesis 1 fourth right parenthesis equals 3 over 8 plus 2 over 8 plus 6 over 8 equals 11 over 8 end cell row blank cell sigma squared equals E left parenthesis x squared right parenthesis minus left parenthesis E left parenthesis x right parenthesis right parenthesis squared equals 0 squared left parenthesis 1 fourth right parenthesis plus 1 squared left parenthesis 3 over 8 right parenthesis plus 2 squared left parenthesis 1 over 8 right parenthesis plus 3 squared left parenthesis 1 fourth right parenthesis minus left parenthesis 11 over 8 right parenthesis squared end cell row blank cell equals 0 plus 3 over 8 plus 4 over 8 plus 9 over 8 minus 121 over 64 equals 16 over 8 minus 121 over 64 equals 7 over 64 end cell row blank blank end table end style

 

أتحقق من فهمي صفحة 86

ميناء: يمثل الاقتران: begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell E left parenthesis x right parenthesis equals sum x p left parenthesis x right parenthesis equals 0 left parenthesis 1 fourth right parenthesis plus 1 left parenthesis 3 over 8 right parenthesis plus 2 left parenthesis 1 over 8 right parenthesis plus 3 left parenthesis 1 fourth right parenthesis equals 3 over 8 plus 2 over 8 plus 6 over 8 equals 11 over 8 end cell row blank cell sigma squared equals E left parenthesis x squared right parenthesis minus left parenthesis E left parenthesis x right parenthesis right parenthesis squared equals 0 squared left parenthesis 1 fourth right parenthesis plus 1 squared left parenthesis 3 over 8 right parenthesis plus 2 squared left parenthesis 1 over 8 right parenthesis plus 3 squared left parenthesis 1 fourth right parenthesis minus left parenthesis 11 over 8 right parenthesis squared end cell row blank cell equals 0 plus 3 over 8 plus 4 over 8 plus 9 over 8 minus 121 over 64 equals 16 over 8 minus 121 over 64 equals 7 over 64 end cell row blank blank end table end style ارتفاع الماء (بالأقدام) عند رصيف أحد الموانىء بعد  ساعة تلي الساعة 6 a.m. . أجد معدل تغيّر ارتفاع الماء عند الرصيف بالنسبة إلى الزمن t .

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell E left parenthesis x right parenthesis equals sum x p left parenthesis x right parenthesis equals 0 left parenthesis 1 fourth right parenthesis plus 1 left parenthesis 3 over 8 right parenthesis plus 2 left parenthesis 1 over 8 right parenthesis plus 3 left parenthesis 1 fourth right parenthesis equals 3 over 8 plus 2 over 8 plus 6 over 8 equals 11 over 8 end cell row blank cell sigma squared equals E left parenthesis x squared right parenthesis minus left parenthesis E left parenthesis x right parenthesis right parenthesis squared equals 0 squared left parenthesis 1 fourth right parenthesis plus 1 squared left parenthesis 3 over 8 right parenthesis plus 2 squared left parenthesis 1 over 8 right parenthesis plus 3 squared left parenthesis 1 fourth right parenthesis minus left parenthesis 11 over 8 right parenthesis squared end cell row blank cell equals 0 plus 3 over 8 plus 4 over 8 plus 9 over 8 minus 121 over 64 equals 16 over 8 minus 121 over 64 equals 7 over 64 end cell row blank blank end table end style

إعداد : شبكة منهاجي التعليمية

10 / 07 / 2023

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