# 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