Pertanyaan

Jika dengan , q = x sin y sin z , dan r = x cos z , tentukanlah ∂ z ∂ w ​ ∣ ∣ ​ x = 2 , y = π , z = 2 π ​ ​

Jika w equals p squared q plus r squared dengan p equals x space cos space y space sin space z, dan , tentukanlah

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai

nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator partial differential w over denominator partial differential z end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table 

Pembahasan

Aturan perkalian pada turunan: Aturan rantai pada turunan: Turunan fungsi trigonometri: Penyelesaian soal di atas adalah sebagai berikut. Dengan demikian, nilai

Aturan perkalian pada turunan:

f open parentheses x close parentheses equals u open parentheses x close parentheses times v open parentheses x close parentheses space rightwards arrow space f apostrophe open parentheses x close parentheses equals u apostrophe open parentheses x close parentheses times v open parentheses x close parentheses plus u open parentheses x close parentheses times v apostrophe open parentheses x close parentheses

Aturan rantai pada turunan:

f open parentheses x close parentheses equals open parentheses u open parentheses x close parentheses close parentheses to the power of n space rightwards arrow space f apostrophe open parentheses x close parentheses equals n times open parentheses u open parentheses x close parentheses close parentheses to the power of n minus 1 end exponent times u apostrophe open parentheses x close parentheses

Turunan fungsi trigonometri:

f open parentheses x close parentheses equals sin space x space rightwards arrow space f apostrophe open parentheses x close parentheses equals cos space x

f open parentheses x close parentheses equals cos space x space rightwards arrow space f apostrophe open parentheses x close parentheses equals negative sin space x

Penyelesaian soal di atas adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row w equals cell p squared q plus r squared end cell row w equals cell open parentheses x space cos space y space sin space z close parentheses squared open parentheses x space sin space y space sin space z close parentheses plus open parentheses x space cos space z close parentheses squared end cell end table

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator partial differential w over denominator partial differential z end fraction end cell equals cell 2 open parentheses x space cos space y space sin space z close parentheses open parentheses x space cos space y space cos space z close parentheses open parentheses x space sin space y space sin space z close parentheses plus end cell row blank blank cell open parentheses x space cos space y space sin space z close parentheses squared open parentheses x space sin space y space cos space z close parentheses plus 2 open parentheses x space cos space z close parentheses open parentheses x open parentheses negative sin space z close parentheses close parentheses end cell row blank equals cell 2 open parentheses 2 times cos space straight pi times sin space straight pi over 2 close parentheses open parentheses 2 times cos space straight pi times cos space straight pi over 2 close parentheses open parentheses 2 times sin space straight pi times sin space straight pi over 2 close parentheses plus end cell row blank blank cell open parentheses 2 times cos space straight pi times sin space straight pi over 2 close parentheses squared open parentheses 2 times sin space straight pi times cos space straight pi over 2 close parentheses end cell row blank blank cell plus 2 open parentheses 2 times cos space straight pi over 2 close parentheses open parentheses negative 2 times sin space straight pi over 2 close parentheses end cell row blank equals cell 2 open parentheses 2 times open parentheses negative 1 close parentheses times 1 close parentheses open parentheses 2 times open parentheses negative 1 close parentheses times 0 close parentheses open parentheses 2 times 0 times 1 close parentheses plus end cell row blank blank cell open parentheses 2 times open parentheses negative 1 close parentheses times 1 close parentheses squared open parentheses 2 times 0 times 0 close parentheses plus 2 open parentheses 2 times 0 close parentheses open parentheses negative 2 times 1 close parentheses end cell row blank equals cell 2 open parentheses negative 2 close parentheses open parentheses 0 close parentheses open parentheses 0 close parentheses plus open parentheses negative 2 close parentheses squared open parentheses 0 close parentheses plus 2 times open parentheses 0 close parentheses open parentheses negative 2 close parentheses end cell row blank equals cell 0 plus 0 plus 0 end cell row blank equals 0 end table end style

Dengan demikian, nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator partial differential w over denominator partial differential z end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table 

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