Differentiation of Trigonometric Functions (مشتقات الدوال المثلثية)

Differentiation of Trigonometric Functions (مشتقات الدوال المثلثية)

إن إشتقاق الدوال المثلثية هو العملية الرياضية لإيجاد مشتقة دالة مثلثية أو معدل تغييرها بالنسبة إلى المتغير. على سبيل المثال، مشتقة دالة الجيب هي دالة الكوساين : sin′(A) = cos(A) مما يعني أن معدل تغير sin(x) في زاوية معينة x = a معطى بواسطة جيب تمام تلك الزاوية.

يمكن العثور على جميع مشتقات الدوال المثلثية الدائرية من خلال دالتي الـِ sin(x) و cos(x) بواسطة قاعدة ناتج القسمة المطبقة على الدوال مثل

tan(x) = sin(x)/cos(x)

من معرفة هذه المشتقات، نستطيع إيجاد مشتقات الدوال المثلثية العكسية باستخدام التمايز الضمني.

مشتقات النسب المثلثية والمثلثية الزائدية

مشتقات النسب المثلثية والمثلثية الزائدية

مشتقات النسب المثلثية العكسية والمثلثية الزائدية العكسية

مشتقات النسب المثلثية العكسية والمثلثية الزائدية العكسية

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