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 3 x plus x to the power of 4 over denominator 2 x squared plus 1 end fraction

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Asked by Topperlearning User | 16th Nov, 2016, 03:31: AM

Expert Answer:

fraction numerator d over denominator d x end fraction f left parenthesis x right parenthesis
equals fraction numerator d over denominator d x end fraction open parentheses fraction numerator 3 x plus x to the power of 4 over denominator 2 x squared plus 1 end fraction close parentheses
equals fraction numerator left parenthesis 2 x squared plus 1 right parenthesis fraction numerator d over denominator d x end fraction open parentheses 3 x plus x to the power of 4 close parentheses minus open parentheses 3 x plus x to the power of 4 close parentheses fraction numerator d over denominator d x end fraction open parentheses 2 x squared plus 1 close parentheses over denominator open parentheses 2 x squared plus 1 close parentheses squared end fraction
equals fraction numerator left parenthesis 2 x squared plus 1 right parenthesis left parenthesis 3 plus 4 x cubed right parenthesis minus open parentheses 3 x plus x to the power of 4 close parentheses left parenthesis 4 x right parenthesis over denominator open parentheses 2 x squared plus 1 close parentheses squared end fraction
equals fraction numerator 4 x to the power of 5 plus 4 x cubed minus 6 x squared plus 3 over denominator open parentheses 2 x squared plus 1 close parentheses squared end fraction

Answered by  | 16th Nov, 2016, 05:31: AM

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