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Berdasarkan ide limit . Tentukan turunan pertama u...

Berdasarkan ide limit f open parentheses x close parentheses equals limit as h rightwards arrow 0 of open square brackets fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction close square brackets. Tentukan turunan pertama untuk masing-masing fungsi berikut. 

  • f open parentheses x close parentheses equals 3 x squared plus 4   

Jawaban:

Diketahui f open parentheses x close parentheses equals 3 x squared plus 4, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x plus h close parentheses end cell equals cell 3 open parentheses x plus h close parentheses squared plus 4 end cell row blank equals cell 3 open parentheses x squared plus 2 x h plus h squared close parentheses plus 4 end cell row blank equals cell 3 x squared plus 6 x h plus 3 h squared plus 4 end cell end table   

Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell 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 end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator open parentheses 3 x squared plus 6 x h plus 3 h squared plus 4 close parentheses minus open parentheses 3 x squared plus 4 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 6 x h plus 3 h squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator h open parentheses 6 x plus 3 h close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of open parentheses 6 x plus 3 h close parentheses end cell row blank equals cell 6 x plus 3 open parentheses 0 close parentheses end cell row blank equals cell 6 x end cell end table   

Jadi, turunan pertama dari f open parentheses x close parentheses equals 3 x squared plus 4 adalah 6 x

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