What is the slope of the tangent line of # 3y^2+4xy+x^2y =C #, where C is an arbitrary constant, at #(2,5)#?
1 Answer
Explanation:
You will need to know the basics of implicit differentiation for this problem.
We know the slope of the tangent line at a point is the derivative; so the first step will be to take the derivative. Let's do it piece by piece, starting with:
This one isn't too hard; you just have to apply the chain rule and power rule:
Now, onto
Alright, finally
Now that we have found all of our derivatives, we can express the problem as:
(Remember the derivative of a constant is
Now we collect terms with
All that's left to do is plug in