Question

Implicit Differentiation
dy/dx x^2y-x-5y-9=0

Answer 1

\[\frac{dy}{dx}x^{2}y-x-5y-9=0\]this?

Answer 2

yes!

Answer 3

okay
so first off we split everything up in terms of differentiation:\[\frac{dy}{dx}(x^{2}y)-\frac{dy}{dx}(x)-\frac{dy}{dx}(5y)-\frac{dy}{dx}(9)=\frac{dy}{dx}(0)\]

Answer 4

(I DON'T KNOW IF THIS IS CORRECT)\[2x\times y'-1-5(1)-9=0\]\[2x\times y'-15=0\]\[2x\times y'=15\]\[y'=\frac{15}{2x}\]

Answer 5

x^2y
product rule

Answer 6

whoops

Answer 7

okay implicit differentiation of \(x^{2}y\) is\[2xy+x^{2}y'\]

Answer 8

so then you have the full implicit differentiation...\[2xy+x^{2}y'-1-5(1)-9=0\]\[2xy+x^{2}y'-15=0\]\[x^{2}y'=-2xy+15...\]\[y=\frac{-2xy+15}{x^{2}}\]

Answer 9

did I get it right? lol

Answer 10

the derivative of constant should be 0

Answer 11

oh gotcha, thank you!!

Answer 12

oh... my bad.

Answer 13

\[2xy+x^{2}y'-1-5(1)-0=0\]\[2xy+x^{2}y'=6\]

Answer 14

\[\large\rm \color{Red}{x^2y} \color{blue}{-x}\color{orange}{-5y}-9=0\]
\[\large\rm \color{Red}{ x^2y= 2x \frac{dx}{dx}(y)+ x^2 (1\frac{dy}{dx} )} \]
\[\color{blue}{-x = -1 \frac{dx}{dx}}\]
\[ \color{orange}{-5y = -5 \frac{dy}{dx}}\]
\[\large\rm \color{Red}{ 2x \frac{dx}{dx}(y)+ x^2 (1\frac{dy}{dx} )} \color{blue}{ -1 \frac{dx}{dx}} \color{orange}{ -5 \frac{dy}{dx}} -0=0\]

dy/dx=taking the derivative of y with respect to x
dx/dx= derivative of x with respect to x

Answer 15

dx/dx=1
so \[\large\rm 2xy+x^2 \frac{dy}{dx}-1 -5\frac{dy}{dx}=0\]
solve for `dy/dx`

Answer 16

@emac
makes sense ?? familiar with the product rule ??