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CBSE Class 11-science Answered

Find the derivative of tanx by first principle !?
Asked by SHAMSUDEEN | 14 Feb, 2015, 01:54: PM
answered-by-expert Expert Answer
F r o m space t h e space f i r s t space p r i n c i p l e comma f apostrophe open parentheses x close parentheses equals limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction space space space space space space space equals limit as h rightwards arrow 0 of fraction numerator tan open parentheses x plus h close parentheses minus tan x over denominator h end fraction space space space space space space space equals limit as h rightwards arrow 0 of fraction numerator begin display style fraction numerator sin open parentheses x plus h close parentheses over denominator cos open parentheses x plus h close parentheses end fraction minus fraction numerator sin x over denominator cos x end fraction end style over denominator h end fraction space space space space space space space equals limit as h rightwards arrow 0 of fraction numerator sin open parentheses x plus h close parentheses cos x minus sin x cos open parentheses x plus h close parentheses over denominator h cos open parentheses x plus h close parentheses cos x end fraction space space space space space space space equals limit as h rightwards arrow 0 of fraction numerator begin display style fraction numerator sin open parentheses 2 x plus h close parentheses plus sin h over denominator 2 end fraction minus fraction numerator sin open parentheses 2 x plus h close parentheses minus sin h over denominator 2 end fraction end style over denominator h cos open parentheses x plus h close parentheses cos x end fraction space space space space space space space equals limit as h rightwards arrow 0 of fraction numerator begin display style sin h end style over denominator h cos open parentheses x plus h close parentheses cos x end fraction space space space space space space space equals limit as h rightwards arrow 0 of fraction numerator begin display style sin h end style over denominator h end fraction cross times space limit as h rightwards arrow 0 of fraction numerator begin display style 1 end style over denominator cos open parentheses x plus h close parentheses cos x end fraction space space space space space space space equals 1 cross times space fraction numerator begin display style 1 end style over denominator cos x cross times cos x end fraction space space space space space space space equals 1 cross times space fraction numerator begin display style 1 end style over denominator cos squared x end fraction space space space space space space space equals s e c squared x
Answered by Vimala Ramamurthy | 14 Feb, 2015, 07:54: PM

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