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

1 Answer
Sep 28, 2016

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 :)