How do you find the slope of the tangent line to the curve $xy^3 + xy = 4$ at the point (2,1)? Thank you! I really, really, appreciate your help:)?

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Answer 1 · 2015-09-26T02:17:26

$slope =-1/4$

$xy^3+xy=4$
$y^3+3xy^2dy/dx+y+xdy/dx=0$
slope at (2,1)
$1+6dy/dx+1+2dy/dx=0$
$8dy/dx=-2$
$dy/dx=-1/4=>slope =-1/4$

How do you find the slope of the tangent line to the curve xy^3 + xy = 4xy^3 + xy = 4 at the point (2,1)? Thank you! I really, really, appreciate your help:)?