Question

Given the relationship x2+3y2=12 and dx/dt=2 units/min, find the value of dy/dt at the instant y=1 unit

Answer 1

so basically your solving a derivative problem right

Answer 2

Implicit differentiation

Answer 3

yea same thing

Answer 4

well the first thing to do would be to take the derivative

Answer 5

Which would be 2xdx/dt+ 6ydy/dt=0

Answer 6

and then i think you would plug in all the info you have and solve for dy/dt

Answer 7

\[x^2+3y^2=12\\2xx'+6yy'=0\] put \(x'=2,y=1\)

Answer 8

So dy/dt=2/3x

Answer 9

you can find x also since
\[x^2+3y^2=12\] and \[y=1\] you get
\[x^2+3=12\\
x^2=9\\
x=\pm 3\]

Answer 10

Oh, okay. So the answer would be -2. Thank you

Answer 11

yw