اوجد د4ص/دس4 للدالة ص= س+1 /س - 1 حيث س لاتساوى 1 ثم استنتج د ن ص /دس ن

هذة المسألة رقم 53 فى دليل التقويم تفاضل

وارجو من سيادتكم حل المسألأة فى اسرع وقت ممكن عشان انا محتاج اخلص المناهج بسرعة

وشكرا جزيلا وجزاكم الله خيرا

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اوجد د4ص/دس4 للدالة ص= س+1 /س - 1 حيث س لاتساوى 1 ثم استنتج د ن ص /دس ن

هذة المسألة رقم 53 فى دليل التقويم تفاضل

وارجو من سيادتكم حل المسألأة فى اسرع وقت ممكن عشان انا محتاج اخلص المناهج بسرعة

وشكرا جزيلا وجزاكم الله خيرا
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المطلوب : المشتقة الرابعة للدالة ( وهى خارج قسمة )
المشتقة الأولى = - 2 / ( س - 1 ) تربيع
المشتقة الثانية = - 4 / ( س - 1 ) تكعيب
المشتقة الثالثة = - 12 / ( س - 1 ) ^ 4
المشتقة الرابعة = - 48 / ( س - 1 ) ^ 5

ولمعرفة المشتقة النونية :
نلاحظ أن أُس المقام دائماً أكبر من رتبة المشتقة بواحد صحيح أى ( ن + 1 )
وبالنسية لبسط المشتقة الأولى = - 2 × 1 = - 2
وبسط المشتقة الثانية = - 2 × 1 × 2 = - 4
وبسط المشتقة الثالثة = - 2 × 1 × 2 × 3 = - 12
وبسط المشتقة الرابعة = - 2 × 1 × 2 × 3 × 4 = - 48
أى :
بسط الأولى = - 2 × مضروب 1
بسط الثانية = - 2 × مضروب 2
بسط الثالثة = - 2 × مضروب 3
بسط الرابعة = - 2 × مضروب 4
إذن بسط المشتقة النونية = - 2 × مضروب ن

فتكون المشتقة النونية = - 2 × مضروب ن / ( س - 1 ) أُس ( ن + 1 )

متشكر بس حضرتك السالب فى المشتقة التانية والرابعة هيتشال المفروض

http://alyeldeen.com/vb/progs4u/misc/quotes/quot-top-left.gif اقتباس: http://alyeldeen.com/vb/progs4u/misc/quotes/quot-top-right.gif
http://alyeldeen.com/vb/progs4u/misc/quotes/quot-by-left.gif المشاركة الأصلية كتبت بواسطة mido soft http://alyeldeen.com/vb/progs4u/misc/quotes/quot-by-right.gif
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متشكر بس حضرتك السالب فى المشتقة التانية والرابعة هيتشال المفروض
http://alyeldeen.com/vb/progs4u/misc/quotes/quot-bot-left.gif
http://alyeldeen.com/vb/progs4u/misc/quotes/quot-bot-right.gif
كلامك مضبوط وبالتالى بدلاً من - 2 نكتب 2 × ( - 1 ) ^ ن

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