Question

Find the derivative y’(x) implicitly. x^2 y^2 + 3y = 4x

Answer 1

@wio can u help?

Answer 2

Sure, what part are you having trouble with?

Answer 3

how do i do it? i already started but i'm stuck so i found the derivative.... f'(x) = 2x y^2 + 3 = 4 is that correct?

Answer 4

Nope.

Answer 5

ohh how do i do it then?

Answer 6

For example: \[
\frac{d}{dx}3y = 3\frac{dy}{dx}
\]

Answer 7

ok

Answer 8

\[x^2y^2 + 3y =4x\] So now the first part is product rule. and you get \[(2xy^2 + 2x^2y \frac{ dy }{ dx }) + 3\frac{ dy }{ dx } = 4\] From there, collect the dy/dx terms on the left, and move the others to the right\[\frac{ dy }{ dx }(2x^2y + 3) = 4-2xy^2\]From there, you divide by the dy/dx term and you get\[\frac{ dy }{ dx }= \frac{ 4-2xy^2 }{ 2x^2y + 3 }\]

Answer 9

\[
x^2 y^2 = \frac{d}{dx}[x^2]y^2+x^2\frac{d}{dx}y^2 = 2xy^2+x^22y\frac{dy}{dx}
\]

Answer 10

okay

Answer 11

Do you understand what is going on?

Answer 12

When finding the derivative for a function of \(y\), you have to use properties of derivatives, such as chain rule.

Answer 13

okay i got you