Question

The slope of the tangent to the curve y^3x + y^2x^2 = 6 at (2,1)

Answer 1

\[(y^3x)'=3y^2y'x+y^3(1)\]
remember (y)'=y'
\[(y^2x^2)'=2yy'x^2+y^2(2x)\]
\[(6)'=0\]

Answer 2

Then find the slope of the tangent line by taking the first derivative implicitly.

Answer 3

all we need is the slope

Answer 4

myininaya is correct!!!Sorry

Answer 5

\[(3y^2y'x+y^3)+(2yy'x^2+y^2(2x))=0\]

Answer 6

I was giving directions on finding the equation of the tangent line

Answer 7

i just plugged in those parts i found above

Answer 8

right pross finding the equation of the tangent line is useful too

Answer 9

so solve what I have for y'
and then plug in x=2 and y=1