Question

Can someone help with a derivative problem?

Answer 1

The question asked to find the line that passes through the given point and has the given slope

Answer 2

\[\Large y'=\frac{ 2y }{ 3x }\]
Point \[\Large (8,2) \]

Answer 3

I got that y=\[\Huge Cx^{\frac{2}{3}}\]

Answer 4

I just need help in taking the derivative and converting to what i got b4

Answer 5

@ganeshie8 @whpalmer4 please hellp

Answer 6

I also got the equation to be y=1/2(x^(2/3))

Answer 7

first observation : x^2/3 is not a line

Answer 8

this problem is simple,
just evaluate the slope at (8, 2)

and use point slope form for writing the equation of line ?

Answer 9

My bad, it says find the equation of the graph

Answer 10

differential equation ?

Answer 11

I got the equation, that's not what I'm asking, I want to take the derivative of this function and get hte same formula I started with to check the \[\Large \frac{2y}{3x}\]

Answer 12

But if I take the derivative of that, I get an explicit function not an implicit

Answer 13

Okay, got u :)

Answer 14

Oh wait......I solved my own problem

Answer 15

The general solution is \[\Large y=Cx^{\frac{ 2 }{ 3 }}\]

Answer 16

\[\Large y~\prime=\frac{ 2c }{ 3\sqrt[3]{x} }\]

Answer 17

\[\Large \frac{ 2c }{ 3\sqrt[3]{x} }~\times \frac{ \sqrt[3]{x} }{ \sqrt[3]{x}}~\times \frac{ \sqrt[3]{x} }{ \sqrt[3]{x} }=\frac{ 2Cx^\frac{ 2 }{ 3 } }{ 3x}\]

Answer 18

But \[\Large y=Cx^{\frac{ 2 }{ 3 }}\]

Answer 19

So its just \[\Large y'=\frac{ 2y }{ 3x }\] correct @ganeshie8 ?

Answer 20

Looks great !!

Answer 21

Thanks!

Answer 22

np :)