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Turunkan masing - masing ekspresi berikut terhadap t. a.  t​3t2−4t​

Pertanyaan

Turunkan masing - masing ekspresi berikut terhadap t.

a.  begin mathsize 14px style fraction numerator 3 t squared minus 4 t over denominator square root of t end fraction end style

S. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

turunan dari fraction numerator 3 t squared minus 4 t over denominator square root of t end fraction adalah 9 t minus 4.

Pembahasan

Ingat bahwa:

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell a times x to the power of n space left right double arrow space f apostrophe left parenthesis x right parenthesis equals a times n times x to the power of n minus 1 end exponent end cell row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator u left parenthesis x right parenthesis over denominator v left parenthesis x right parenthesis end fraction space left right double arrow space f apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe left parenthesis x right parenthesis v left parenthesis x right parenthesis minus v apostrophe left parenthesis x right parenthesis u left parenthesis x right parenthesis over denominator open parentheses v left parenthesis x right parenthesis close parentheses squared end fraction end cell end table

Diketahui fraction numerator 3 t squared minus 4 t over denominator square root of t end fraction maka diperoleh

u left parenthesis t right parenthesis equals 3 t squared minus 4 t space left right double arrow space u apostrophe left parenthesis t right parenthesis equals 6 t minus 4 v left parenthesis t right parenthesis equals square root of t space left right double arrow space v apostrophe left parenthesis t right parenthesis equals fraction numerator 1 over denominator 2 square root of t end fraction

Sehingga turunannya adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open parentheses 6 t minus 4 close parentheses open parentheses square root of t close parentheses minus open parentheses begin display style fraction numerator 1 over denominator 2 square root of t end fraction end style close parentheses open parentheses 3 t squared minus 4 t close parentheses over denominator open parentheses square root of t close parentheses squared end fraction end cell row blank equals cell fraction numerator 6 t square root of t minus 4 square root of t minus begin display style fraction numerator 3 t squared minus 4 t over denominator 2 square root of t end fraction end style over denominator t end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 square root of t open parentheses 6 t square root of t minus 4 square root of t close parentheses over denominator 2 square root of t end fraction end style minus fraction numerator 3 t squared minus 4 t over denominator 2 square root of t end fraction over denominator t end fraction end cell row blank equals cell fraction numerator 12 t squared minus 8 t minus 3 t squared plus 4 t over denominator t end fraction end cell row blank equals cell fraction numerator 9 t squared minus 4 t over denominator t end fraction end cell row blank equals cell fraction numerator t left parenthesis 9 t minus 4 right parenthesis over denominator t end fraction end cell row blank equals cell 9 t minus 4 end cell end table

Dengan demikian, turunan dari fraction numerator 3 t squared minus 4 t over denominator square root of t end fraction adalah 9 t minus 4.

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