Example 26 (iii) - Chapter 5 Class 12 Continuity and Differentiability

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Example 26 (iii) - Differentiate cos^-1 (e^x) - Inverse Differentiatio - Examples

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Example 26 Differentiate the following w.r.t. x: (iii) 怖š‘š‘œš‘ ć€—^(āˆ’1) "(ex)" Let š‘¦ = 怖š‘š‘œš‘ ć€—^(āˆ’1) "(ex)" Differentiating both sides š‘¤.š‘Ÿ.š‘”.š‘„ š‘‘š‘¦/š‘‘š‘„ = š‘‘(cos^(āˆ’1)ā”(š‘’^š‘„ ) )/š‘‘š‘„ š‘‘š‘¦/š‘‘š‘„ = (āˆ’1)/āˆš(1 āˆ’ (š‘’^š‘„ )^2 ) . š‘‘(š‘’^š‘„ )/š‘‘š‘„ š‘‘š‘¦/š‘‘š‘„ = (āˆ’1)/āˆš(1 āˆ’ (š‘’^š‘„ )^2 ) . š‘’^š‘„ š’…š’š/š’…š’™ = (āˆ’š’†^š’™)/āˆš(šŸ āˆ’ š’†^šŸš’™ ) (As (cos^(āˆ’1)ā”š‘„ )^ā€²=(āˆ’1)/āˆš(1 āˆ’ š‘„^2 )) (As(š‘’^š‘„ )^ā€²=š‘’^š‘„)

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