Relevant page
<a href="/integration/integration-mini-lecture-find-y-given-dy-dx.php">7c. Given dy/dx, find y = f(x)</a>
What I've done so far
Watched the videos and read some of the pages. But I'm lost

Post your solution so we can see how you went. I encourage you to use the math entry system to make your math easier to read.

X

Hi Oscar
There are examples similar to your question on this Implicit Differentiation page:
<a href="/differentiation/8-derivative-implicit-function.php">8. Differentiation of Implicit Functions</a>
Is that enough to get you started?
Post your solution so we can see how you went. I encourage you to use the math entry system to make your math easier to read.

For interest just now, I graphed your implicit function and noticed a problem.

The graph doesn't even go through the point `(600, 200)`!

This is a case where we can calculate an answer, but it doesn't have any meaning.

As you can see, the graph as `x` gets very big (and goes off in the negative direction) has slope very close to `-1`.

When we substitute `x=200` into the original equation, we get `y^2+40000y+7999708 = 0` and this has solutions `y=-39799` or `y=-201.0`.

The slope is steeply negative for the first one, and very close to `-1` for the second.

Graphs tell us a lot about what is going on!

X

For interest just now, I graphed your implicit function and noticed a problem.
<img src="/forum/uploads/imf-4548-x3x2yy2is292-graph.png" width="410" height="498" alt="How to differentiate?" />
The graph doesn't even go through the point `(600, 200)`!
This is a case where we can calculate an answer, but it doesn't have any meaning.
As you can see, the graph as `x` gets very big (and goes off in the negative direction) has slope very close to `-1`.
When we substitute `x=200` into the original equation, we get `y^2+40000y+7999708 = 0` and this has solutions `y=-39799` or `y=-201.0`.
The slope is steeply negative for the first one, and very close to `-1` for the second.
Graphs tell us a lot about what is going on!