Question

How do you use implicit differentiation to find dy/dx given `y^4=x^2-6x+2`?

Answer 1

The answer is `(2x - 6)/(4y^3)`

Explanation:

So, the main thing to remember is that with implicit differentiation, when you take a derivative of something that's not an `x`, you need to do the following steps:

1. Take the derivative as normal.
2. Tag on a `dy/dx`

Then, to solve the problem, you'd just have to solve for the `dy/dx`

The only place this is really applicable in this particular example is with the `y^4`. So applying the above to this, we'd get `4y^3dy/dx`.

We can find the derivatives for the other terms using simple power rule. This leaves us with:

`4y^3dy/dx = 2x - 6`

Now, we just divide both sides by `4y^3` to solve for the `dy/dx`, and that leaves us with `dy/dx = (2x - 6)/(4y^3)`, and we are done!

Hope that helps :)