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3. Tentukan  dari fungsi-fungsi berikut. b.

Pertanyaan

3. Tentukan f apostrophe open parentheses x close parentheses dari fungsi-fungsi berikut.

b. f open parentheses x close parentheses equals fraction numerator sin space x plus cos space x over denominator sin space x minus cos space x end fraction  

Pembahasan Soal:

Turunan fungsi f open parentheses x close parentheses equals sin space g open parentheses x close parentheses yaitu f apostrophe open parentheses x close parentheses equals cos space g open parentheses x close parentheses space g apostrophe open parentheses x close parentheses, dan turunan fungsi f open parentheses x close parentheses equals cos space g open parentheses x close parentheses yaituf apostrophe open parentheses x close parentheses equals negative sin space g open parentheses x close parentheses space g apostrophe open parentheses x close parentheses.

Aturan pembagian pada turunan yaitu sebagai berikut:

 f open parentheses x close parentheses equals u over v f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction 

Untuk menyelesaikan soal di atas, perhatikan penghitungan berikut:

    f open parentheses x close parentheses equals fraction numerator sin space x plus cos space x over denominator sin space x minus cos space x end fraction u equals sin space x plus cos space x rightwards arrow u apostrophe equals cos space x minus sin space x v equals sin space x minus cos space x rightwards arrow v apostrophe equals cos space x minus open parentheses negative sin space x close parentheses equals cos space x plus sin space x  f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction f apostrophe open parentheses x close parentheses equals fraction numerator open parentheses cos space x minus sin space x close parentheses open parentheses sin space x minus cos space x close parentheses minus open parentheses sin space x plus cos space x close parentheses open parentheses cos space x plus sin space x close parentheses over denominator open parentheses sin space x minus cos space x close parentheses squared end fraction f apostrophe open parentheses x close parentheses equals fraction numerator up diagonal strike cos space x space sin space x end strike minus cos squared space x minus sin squared space x plus up diagonal strike sin space x space cos space x end strike minus up diagonal strike sin space x space cos space x end strike minus sin squared space x minus cos squared space x minus up diagonal strike cos space x space sin space x end strike over denominator open parentheses sin space x minus cos space x close parentheses squared end fraction f apostrophe open parentheses x close parentheses equals fraction numerator negative cos squared space x minus sin squared space x minus sin squared space x minus cos squared space x over denominator open parentheses sin space x minus cos space x close parentheses squared end fraction f apostrophe open parentheses x close parentheses equals fraction numerator negative open parentheses cos squared space x plus sin squared space x close parentheses minus open parentheses sin squared space x plus cos squared space x close parentheses over denominator open parentheses sin space x minus cos space x close parentheses squared end fraction f apostrophe open parentheses x close parentheses equals fraction numerator negative 1 minus 1 over denominator open parentheses sin space x minus cos space x close parentheses squared end fraction f apostrophe open parentheses x close parentheses equals fraction numerator negative 2 over denominator open parentheses sin space x minus cos space x close parentheses squared end fraction      

Jadi, turunannya adalah f apostrophe open parentheses x close parentheses equals fraction numerator negative 2 over denominator open parentheses sin space x minus cos space x close parentheses squared end fraction.    space 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Juli 2021

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