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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 space 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 square root of 1 minus 9 x end root

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Asked by Topperlearning User 16th November 2016, 2:41 AM
Answered by Expert
Answer:

space f left parenthesis x right parenthesis equals square root of 1 minus 9 x end root
f left parenthesis x plus h right parenthesis equals square root of 1 minus 9 left parenthesis x plus h right parenthesis end root
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 square root of 1 minus 9 left parenthesis x plus h right parenthesis end root minus square root of 1 minus 9 x end root over denominator h end fraction
equals limit as h rightwards arrow 0 of fraction numerator square root of 1 minus 9 left parenthesis x plus h right parenthesis end root minus square root of 1 minus 9 x end root over denominator h end fraction open parentheses fraction numerator square root of 1 minus 9 left parenthesis x plus h right parenthesis end root plus square root of 1 minus 9 x end root over denominator square root of 1 minus 9 left parenthesis x plus h right parenthesis end root plus square root of 1 minus 9 x end root end fraction close parentheses
equals limit as h rightwards arrow 0 of fraction numerator 1 minus 9 left parenthesis x plus h right parenthesis minus 1 plus 9 x over denominator h left parenthesis square root of 1 minus 9 left parenthesis x plus h right parenthesis end root plus square root of 1 minus 9 x end root right parenthesis end fraction
equals limit as h rightwards arrow 0 of fraction numerator negative 9 h over denominator h left parenthesis square root of 1 minus 9 left parenthesis x plus h right parenthesis end root plus square root of 1 minus 9 x end root right parenthesis end fraction
equals fraction numerator negative 9 over denominator 2 square root of 1 minus 9 x end root end fraction

Answered by Expert 16th November 2016, 4:41 AM
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