Q. aa[tex] \\ [/tex][tex] \tt \: hasil \: \frac{dy}{dx} \: dari \: pers \: {x}^{3} + x

May 2022 2 16 Report

Q. aa
[tex] \\ [/tex]
[tex] \tt \: hasil \: \frac{dy}{dx} \: dari \: pers \: {x}^{3} + x - y = {x}^{2} \: adalah...[/tex]
[tex] \\ [/tex]
[tex] \tt \: a. \: 3 {x}^{2} - 2x + 1[/tex]
[tex] \tt \: b. \: - 3 {x}^{2} + 2x + 1[/tex]
[tex] \tt \: c. \: 3 {x}^{2} + 2x - 1[/tex]
[tex] \tt \: d. \: 3 {x}^{2} - x + 2[/tex]
[tex] \tt \: e. \: 3 {x}^{2} + x - 2[/tex]
[tex] \\ [/tex]
RULES ✏ :
[tex] \\ [/tex]
➪ Sertakan Cara-!
➪ No Ngasal-!
➪ No Copas-!
➪ Rapi.
[tex] \\ [/tex]
Trims.

henriyulianto

$\displaystyle \frac{dy}{dx} = \bf3x^2-2x+1$

(opsi a)

Pembahasan

Turunan

$\begin{aligned}&x^3+x-y=x^2\\&{\Rightarrow\ }y=x^3-x^2+x\\\\&{\Rightarrow\ }\frac{dy}{dx}=\frac{d}{dx}\left(x^3-x^2+x\right)\\&{\qquad\quad\!\!}=\frac{d}{dx}x^3\:-\:\frac{d}{dx}x^2\:+\:\frac{d}{dx}x\\&{\qquad\quad\!\!}=3x^{3-1}\:-\:2x^{2-1}\:+\:1x^{1-1}\\\\&{\therefore}\ \ \frac{dy}{dx}=\boxed{\ \bf3x^2-2x+1\ }\end{aligned}$

7 votes Thanks 7

HayabusaBrainly01

Jawaban:

Opsi A.

Penjelasan dengan langkah-langkah:

${x}^{3} + x - y = {x}^{2} \\ - y = {x}^{2} - {x}^{3} - x \\ y = - ( {x}^{2} - {x}^{3} - x \\ y = - {x}^{2} + {x}^{3} + x \\ y = {x}^{3} - {x}^{2} + x$