TURUNAN FUNGSI ALJABAR_3

Presentation

•

Mathematics

•

11th Grade

•

Hard

Mawaddah Amsul

Used 3+ times

FREE Resource

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

Show answer

Auto Play

Slide 1 / 7

SLIDE

Similar Resources on Wayground

7 questions

Composition of Functions Day 1

Presentation

•

11th Grade

3 questions

Semelhança de Triângulos 2

Presentation

•

11th Grade

7 questions

Teoría: Función Inversa

Presentation

•

11th Grade

7 questions

АОЗ_Первісна та її властивості

Presentation

•

11th Grade

6 questions

MATEMÁTICA

Presentation

•

11th Grade

6 questions

OPERACIONES COMBINADAS

Presentation

•

11th Grade

6 questions

Sistem Koordinat Kartesius dan Sistem Koordinat Polar

Presentation

•

11th Grade

6 questions

Barisan Deret

Presentation

•

11th Grade

Popular Resources on Wayground

10 questions

Safety Day 2026 – Student Review

Quiz

•

9th Grade

21 questions

Continents and Oceans

Quiz

•

6th Grade

20 questions

Parts of Speech

Quiz

•

5th Grade

16 questions

Subject & Predicate

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

Map Skills

Quiz

•

3rd Grade

22 questions

Continents and Oceans

Quiz

•

5th Grade

15 questions

Rounding Decimals

Quiz

•

5th Grade

Discover more resources for Mathematics

12 questions

Identify Rigid Transformations

Quiz

•

8th - 12th Grade

10 questions

Complementary, Supplementary, Vertical, and Linear Pairs

Quiz

•

9th - 12th Grade

22 questions

Identify Vertical and Horizontal Translations

Quiz

•

9th - 12th Grade

10 questions

Graphing Inequalities on a Number Line

Quiz

•

9th - 12th Grade

17 questions

Identifying Parallel And Perpendicular Lines

Quiz

•

9th - 12th Grade

18 questions

Integer Operations

Quiz

•

5th - 12th Grade

18 questions

Parallel lines cut by a transversal

Quiz

•

9th - 11th Grade

14 questions

Evaluate Linear Functions and Their Applications

Quiz

•

9th - 12th Grade