مطبوعــــات الإبداع في الرياضيات
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التفـــــاضل (1 - 2)
القواعد الأساسية للتفاضل :
1- إذا كانت د(س) = أ حيث أ ثابت فإن : د/(س) = = صفر .
2- إذا كانت ص = أس ( أ ثابت ) فإن : = أ .
3- إذا كانت ص = سن ( حيث ن ح ) فإن : = ن سن – 1 .
4- إذا كانت ص = أسن فإن : = أ ن سن – 1 .
المشتقة الأولى للمجموع الجبري لدالتين :
إذا كانت ع ، ق دالتين في س . وكانت كل منهما قابله للإشتقاق عند س فإن الدالة
ص = ع ق تكون قابلة للإشتقاق عند س ، يكون :
= أي ( ع ق ) =
هذه النتيجة صحيحة لأي عدد منته من الدوال
مشتقة حاصل ضرب دالتين
إذا كانت ع = ر(س) ، ل = ق(س) ، ص = ع ل =ر(س) .ق(س) فإن :
= ع × + ل ×
مشتقة حاصل قسمة دالتين
إذا كانت ع = ر(س) ، ل = ق(س) ص = = فإن :
ل × - ع×
ل2
مشتقة دالة الدالة :
إذا كانت ص = [ د(س) ]ن فإن : = ن(د(س))ن – 1 ×د/(س) .
مشتقة الدوال المثلثية
إذا كان ص = جاس فإن = جتاس.
إذا كان ص = جتاس فإن = -جاس .
إذا كان ص = ظاس فإن = قا2س .
مسائل منوعة
جد المشتقة الاولى من المبادئ الأولية للدوال التالية :
(i) ص = س5
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(ii) ص =
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(iii) ص = س2 – 5
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(iv) ص = س
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(v) ص = س2 + س + 1
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جد للدوال التالية :
(أ) 1/ ص = 6- س3 + جاس
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2/ ص = 1+ س + جاس
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3/ ص = س + ظتا2س
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4/ ص = س3 + 5س2
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5/ ص = 4س3 +2س –
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6/ ص = - +
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7/ ص = +
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(ب) 1/ ص = س جاس
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2/ ص= 4س2 ( 3 – 4س )
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3/ ص = (2س+5)(س2 + 3س+1)
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4/ ص = س3 جاس
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5/ ص = جاس جتا2س
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6/ ص = س2ظا2س
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(ج) 1/ ص =
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2/ ص =
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3/ ص=
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(د) 4/ ص = (2س2 – 1) 5
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2/ ص= (2س – 3 ) 4
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3/ ص= 3س2 + 2
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4/ ص = جا(2-3س)
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5/ ص = جتا(2س2 +1)
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6/ ص = جتا2س
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7/ ص =
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8/ ص =
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9/ ص =
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(هـ) 1/ ص = (2س2 +3)( 1-3س)3
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2/ ص =
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3/ ص = س س2 – 4
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4/ ص =
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موضوع: القواعد الاساسية للتفاضل 
الأربعاء 29 أغسطس 2012 - 10:25
