Explanation Given: The function, f ( t ) = 1 + tan t 3 . Concept Used: Chain rule, d d x ( f ( g ( x ) ) ) = f ' ( g ( x ) ) ⋅ g ' ( x ) Power rule of derivatives, d d x ( x n ) = n x n − 1 d d x ( tan x ) = sec 2 x Derivative of any constant C is zero, that is, d d x ( C ) = 0 Exponent rule: a n = a 1 / n Calculation: In order to find the derivative of the function, first rewrite the function in exponential form using the exponent rule and then use chain rule and power rule of derivatives to simplify further as, f ' ( t ) = d d t ( 1 + tan t 3 ) = d d t ( 1 + tan t ) 1 / 3

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ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Chapter 3.5, Problem 12E

To determine

The derivative of the function, f(t)=1+tant3 .

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Chapter 3.5, Problem 11E

Chapter 3.5, Problem 13E

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٣:٥٣ النموذج الاول . . . O O O بشما ند الحمر الحمر الجمهورية الجنية وزارة التربية والتعليم اليوم التاريخ اللجنة العليا للاختبارات الزمن اختبار مادة الجبر والهندسة لجنة المطابع السرية المركزية للشهادة الثانوية العامة (القسم العلمي) الفترة %97 (1) ظلل في ورقة الإجابة الدائرة التي تحتوي على الحرف ( ص ) للإجابة الصحيحة والحرف ( خ ) للإجابة الخطأ بحسب رقم الفقرة لكل مما يأتي ( درجة لكل فقرة ) )1 ) 2 ) 3 ) 4 ) بؤرة القطع س" = ١٢ ص هي ( ۲ ) طول المحور الأصغر للقطع ٩ س + ص = ٩ يساوي 6 وحدات طول . ) إذا كان & عدد مركب ، 181 + 11 = ٦ ، فإن ١١ = ٣ . ) إذا كان م + ۳ ت = ۲ + ت ب م ، ب دع ، فإن م + ب = 5 ( ) إذا كان & = ۱ + ٣ ت ، فإن ٠ = ١٠ . 6 ( - ) إذا كان ٥٠ - ٣ - ١٢٠ ٤ - ٣ ، فإن قيمة ٧ = ٥ . 1 ) = N ) إذا كان ح هو الحد الخالي من س في المفكوك ( س + v. N 8 ( ( قيمة المقدار , = + ۱ ، * . . + ، فإن قيمة ٧ = ١٦ . ۱ + 9 ( ) المستقيمان المقاربان للقطع الذي معادلته س" = ١ هما ص = : ۹ 10 ( ) إذا كان ٥ + س = ٢٤ ، فإن قيمة س = - 1 س 11 ( ) إذا كانت النسبة بين الحدين الأوسطين تساوي 9 في المفكوك ( س + - ) ،…

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The derivative of the function, f ( t ) = 1 + tan t 3 .

Solution Summary: The author explains how to find the derivative of the function by rewriting it in exponential form and using chain rule and power rule of derivatives.

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The derivative of the function, f(t)=1+tant3 .

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Chapter 3 Solutions