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untuk

begin mathsize 14px style straight f open parentheses straight x close parentheses equals open parentheses 7 minus straight x close parentheses square root of 4 straight x plus 1 end root end style untuk begin mathsize 14px style straight x equals 1 end style 

  1. ...space 

  2. ...space space 

Jawaban:

Turunan fungsi f(x) dapat kita notasikan dengan f'(x) dan didefinisikan sebagai:

f apostrophe left parenthesis x right parenthesis space equals space n x ⁿ ⁻ ¹ space u n t u k space f left parenthesis x right parenthesis space equals space x ⁿ

Apabila terdapat f(x) = u(x)v(x), maka turunan dari f(x) adalah:

f apostrophe left parenthesis x right parenthesis space equals space u apostrophe v space plus space v apostrophe u

dengan u' = turunan dari u(x)

              v' = turunan dari v(x)

Dari soal diketahui f(x) = (7 - 3x)√(4x + 1) maka dimisalkan:

u(x) = 7 - 3 x

v(x) = √(4x + 1)

Kemudian dicari turunan dari u(x) dan v(x)

turunan u(x)

u(x) = 7 - 3x

u' = -3

turunan dari v(x)

 

v left parenthesis x right parenthesis equals √ left parenthesis 4 space x space plus 1 right parenthesis v left parenthesis x right parenthesis equals left parenthesis 4 x plus 1 right parenthesis hat left parenthesis 1 divided by 2 right parenthesis v apostrophe equals 1 divided by 2 left parenthesis 4 x plus 1 right parenthesis hat left parenthesis 1 divided by 2 minus 1 right parenthesis cross times 4 v apostrophe equals 4 divided by 2 left parenthesis 4 x plus 1 right parenthesis hat left parenthesis minus 1 divided by 2 right parenthesis v apostrophe equals 2 divided by √ left parenthesis 4 x plus 1 right parenthesis

 

turunan dari f(x)

 

f apostrophe left parenthesis x right parenthesis space equals space u apostrophe v space plus space v apostrophe u space space f apostrophe left parenthesis x right parenthesis space equals space minus 3 √ left parenthesis 4 x space plus space 1 right parenthesis space plus space 2 divided by √ left parenthesis 4 x space plus space 1 right parenthesis space cross times space left parenthesis 7 space minus space 3 x right parenthesis space space f apostrophe left parenthesis x right parenthesis space equals space minus 3 √ left parenthesis 4 x space plus space 1 right parenthesis space plus space 2 left parenthesis 7 space minus space 3 x right parenthesis divided by √ left parenthesis 4 x space plus space 1 right parenthesis

 

untuk x = 1, maka diperoleh:

 

f apostrophe left parenthesis 1 right parenthesis space equals space minus 3 √ left parenthesis 4 left parenthesis 1 right parenthesis space plus space 1 right parenthesis space plus space 2 left parenthesis 7 space minus space 3 left parenthesis 1 right parenthesis right parenthesis divided by √ left parenthesis 4 left parenthesis 1 right parenthesis space plus space 1 right parenthesis space space f apostrophe left parenthesis 1 right parenthesis space equals space minus 3 √ left parenthesis 4 space plus space 1 right parenthesis space plus space 2 left parenthesis 7 space minus space 3 right parenthesis divided by √ left parenthesis 4 space plus space 1 right parenthesis space space f apostrophe left parenthesis 1 right parenthesis space equals space minus 3 √ 5 space plus space 2 left parenthesis 4 right parenthesis divided by √ 5 space space f apostrophe left parenthesis 1 right parenthesis space equals space minus 3 √ 5 space plus space 8 divided by √ 5 space space f apostrophe left parenthesis 1 right parenthesis space equals space left parenthesis negative 3 √ 5 space cross times space √ 5 right parenthesis divided by √ 5 space plus space 8 divided by √ 5 space space f apostrophe left parenthesis 1 right parenthesis space equals space left parenthesis negative 3 space cross times space 5 right parenthesis divided by √ 5 space plus space 8 divided by √ 5 space space f apostrophe left parenthesis 1 right parenthesis space equals space left parenthesis negative 15 right parenthesis divided by √ 5 space plus space 8 divided by √ 5 space space f apostrophe left parenthesis 1 right parenthesis space equals space minus 7 divided by √ 5 space space f apostrophe left parenthesis 1 right parenthesis space equals space minus 7 divided by 5 space √ 5

Jadi nilai turunan fungsi f(x) = (7 - 3x)√(4x + 1) untuk x = 1 adalah -7/√5 atau -7/5 √5.

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