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F i n d space t h e space d e r i v a t i v e space o f space sin left parenthesis x plus 1 right parenthesis space u sin g space F i r s t space P r i n c i p l e space m e t h o d.

Please provide solution to this question

Asked by Topperlearning User 10th November 2016, 1:35 AM
Answered by Expert
Answer:

f left parenthesis x right parenthesis equals sin left parenthesis x plus 1 right parenthesis
f left parenthesis x plus h right parenthesis equals sin left parenthesis x plus h plus 1 right parenthesis
f to the power of apostrophe left parenthesis x right parenthesis equals limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction
equals limit as h rightwards arrow 0 of fraction numerator sin left parenthesis x plus h plus 1 right parenthesis minus sin left parenthesis x plus 1 right parenthesis over denominator h end fraction
equals limit as h rightwards arrow 0 of fraction numerator 2 cos open parentheses begin display style fraction numerator 2 x plus 2 plus h over denominator 2 end fraction end style close parentheses sin open parentheses begin display style h over 2 end style close parentheses over denominator h end fraction
equals limit as h rightwards arrow 0 of fraction numerator cos open parentheses begin display style x plus 1 plus h over 2 end style close parentheses sin open parentheses begin display style h over 2 end style close parentheses over denominator begin display style h over 2 end style end fraction
equals limit as h rightwards arrow 0 of cos open parentheses x plus 1 plus h over 2 close parentheses limit as h rightwards arrow 0 of fraction numerator sin open parentheses h over 2 close parentheses over denominator h over 2 end fraction space space left square bracket because limit as h rightwards arrow 0 of fraction numerator sin h over denominator h end fraction equals 1 right square bracket
equals cos left parenthesis x plus 1 right parenthesis

Answered by Expert 10th November 2016, 3:35 AM
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