التفاضل 2 -2
الدالة الضمنية
هي الدالة التي يتم فيها التعبير عن قيمة ص بدلالة س بشكل غير مباشر
مسائل منوعة
(i) ص2 = س2 + 5
................................................................................................................................................................................ ................................................................................................................................................................................
(ii) ( 1 – س ) ص = 1 + س
................................................................................................................................................................................
................................................................................................................................................................................
(iii) 2س – 3ص + 7 = 0
................................................................................................................................................................................
................................................................................................................................................................................
(iv) جاس + جاص = ص
................................................................................................................................................................................
................................................................................................................................................................................
(v) س + ص – 4 = 0
................................................................................................................................................................................
................................................................................................................................................................................
(vi) س3 + ص3 = 27
................................................................................................................................................................................
................................................................................................................................................................................
(vii) س ص = 1
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
(viii) ص2 = س ص + 1
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
(ix) س3 + ص3 = 8 س ص2
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
(x) ص2 + س2 + 3س ص = 6
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
(xi) س جاص + ص جاس = 1
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
(xii) ص = جتا( س2 + ص )
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
(xiii) إذا كان س2 – 5س ص + ص2 – 7 = 0 جد عندما س = 1
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
(xiv) س2 + ص2 – 2س – 4ص = 5 جد عند النقطة (2 ، -1)
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
المشتقات العليا
i. إذا كان ص = 2س2 – 5 اثبت ان : س2 – س = صفر
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
ii. ص = جد
................................................................................................................................................................................
................................................................................................................................................................................
iii. ص = جد
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
iv. أس2 + ب س = ص جد المشتقة الثانية
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
v. ص = (س2 + 3)2 اثبت ان : + س - 3 =صفر
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
vi. ص = جتا2س اثبت ان : = 8 عند س =
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
................................................................................................................................................................................
موضوع: الدالة الضمنية والمشتقات العليا 
الأربعاء 29 أغسطس 2012 - 10:20
