# What is the slope of the tangent line of # 3y^2+y/x+x^2/y =C #, where C is an arbitrary constant, at #(2,2)#?

##### 2 Answers

I got

#### Explanation:

Given:

Find: the slope of the tangent line to the graph at the point

Solution:

So

and

Differentiating with respect to

Therefore,

And, so,

#### Explanation:

This can also be done without evaluating the constant and using quotient rule:

#6ydy/dx+(dy/dx(x)-y)/x^2+(2xy-dy/dx(x^2))/y^2=0#

Plug in the point

#12dy/dx+(2dy/dx-2)/4+(8-4dy/dx)/4=0#

#48dy/dx+2dy/dx-2+8-4dy/dx=0#

#46dy/dx=-6#

#dy/dx=-3/23#