TURUNAN FUNGSI ALJABAR_3

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Mathematics

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11th Grade

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Hard

Mawaddah Amsul

Used 3+ times

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5 Slides • 2 Questions

TURUNAN FUNGSI ALJABAR_3

Turunan Bentuk Akar

Untuk mencari turunan dari fungsi yang memuat bentuk akar atau pecahan, langkah pertama yang harus kita lakukan yaitu merubah terlebih dahulu fungsi tesebut kedalam bentuk pangkat (eksponen)

Berikut terdapat beberapa sifat akar dan pangkat yang sering dipakai, anatara lain:

$x^m.\ x^n=x^{m+n}$
$\frac{x^m}{x^n}=\ x^{m-n}$
$\frac{1}{x^n}=\ x^{-n}$
$\sqrt{x}=x^{\frac{1}{2}}$
$^n\sqrt{x^m}=\ x^{\frac{m}{n}}$

Contoh Soal

Tentukan turunan dari $f\left(x\right)=x\sqrt{x}$

Penyelesaian:

f\left(x\right)=x\sqrt{x}\ =x.\ x^{\frac{1}{2}}=x^{\frac{3}{2}}

jadi

f\left(x\right)=x^{\frac{3}{2}}

f'\left(x\right)=\frac{3}{2}x^{\frac{3}{2}-1}

=\frac{3}{2}x^{\frac{1}{2}}

=\frac{3}{2}\sqrt{x}

Contoh Soal

Tentukan turunan dari $f\left(x\right)=\frac{6}{^{3\sqrt{x}}}$

Penyelesaian:

f\left(x\right)=\frac{6}{^{3\sqrt{x}}}\ =6x^{-\frac{1}{3}}

f\left(x\right)=6x^{-\frac{1}{3}}\ \rightarrow\ f'\left(x\right)=6\left(-\frac{1}{3}\right)x^{-\frac{1}{3}-1}

=\ -2x^{-\frac{4}{3}}

=\ -\frac{2}{x^{\frac{4}{3}}}

=\ -\frac{2}{x.x^{\frac{1}{3}}}

=-\frac{2}{x\ ^3\sqrt{x}}

Multiple Choice

Turunan pertama dari fungsi $f\left(x\right)=6x^{\frac{3}{2}}$

$9x^{\frac{3}{2}}$

$9x^{\frac{1}{2}}$

$9x^{-\frac{1}{2}}$

Multiple Choice

Turunan pertama dari fungsi $f\left(x\right)=12\ ^3\sqrt{x^4}$

$16\ ^3\sqrt{x}$

$16\ ^3\sqrt{x^4}$

$16\ \sqrt{x}$

TURUNAN FUNGSI ALJABAR_3

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