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#