Pertanyaan

Tentukan turunan pertama fungsi berikut, sederhanakan jika mungkin. 2 . y = tan − 1 ( e x )

Tentukan turunan pertama fungsi berikut, sederhanakan jika mungkin.

$2$ . $y = tan^{- 1} (e^{x})$

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Klaim

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Teorema turunan fungsi invers trigonometri. Turunan fungsi eksponensialyaitu: Kemudian diperoleh turunannya yaitu: Maka,turunan pertama fungsi adalah .

Teorema turunan fungsi invers trigonometri.

$fraction numerator d over denominator d x end fraction open square brackets tan to the power of negative 1 end exponent space x close square brackets equals fraction numerator 1 over denominator 1 plus x squared end fraction$

Turunan fungsi eksponensial yaitu:

y equals e to the power of x rightwards arrow y apostrophe equals e to the power of x

Kemudian diperoleh turunannya yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row y equals cell tan to the power of negative 1 end exponent space open parentheses e to the power of x close parentheses end cell row cell y apostrophe end cell equals cell fraction numerator 1 over denominator 1 plus open parentheses e to the power of x close parentheses squared end fraction times e to the power of x end cell row cell y apostrophe end cell equals cell fraction numerator e to the power of x over denominator 1 plus e to the power of 2 x end exponent end fraction end cell end table$

Maka, turunan pertama fungsi y equals tan to the power of negative 1 end exponent space open parentheses e to the power of x close parentheses adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator e to the power of x over denominator 1 plus e to the power of 2 x end exponent end fraction end cell end table$ .