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U sin g space t h e space d e f i n i t i o n space o f space d e r i v a t i v e comma f i n d space t h e space d e r i v a t i v e space o f space f left parenthesis x right parenthesis equals fraction numerator x over denominator x plus 1 end fraction

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Asked by Topperlearning User 16th November 2016, 2:49 AM
Answered by Expert
Answer:

f left parenthesis x right parenthesis equals fraction numerator x over denominator x plus 1 end fraction
f left parenthesis x plus h right parenthesis equals fraction numerator x plus h over denominator x plus h plus 1 end fraction
f 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 fraction numerator x plus h over denominator x plus h plus 1 end fraction minus fraction numerator x over denominator x plus 1 end fraction over denominator h end fraction
equals limit as h rightwards arrow 0 of fraction numerator x squared plus x h plus h plus x minus x squared minus x h minus x over denominator h left parenthesis x plus 1 right parenthesis left parenthesis x plus h plus 1 right parenthesis end fraction
equals limit as h rightwards arrow 0 of fraction numerator h over denominator h left parenthesis x plus 1 right parenthesis left parenthesis x plus h plus 1 right parenthesis end fraction
equals fraction numerator 1 over denominator left parenthesis x plus 1 right parenthesis squared end fraction

Answered by Expert 16th November 2016, 4:49 AM
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