Question

Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy = 20 at the point ( 10 , 1 ). Write the equation for the tangent line in the form y = mx+b

Answer 1

@alishabeyer where are you stuck at?

Answer 2

product rule: \[xy^3+xy=20\] taking derivatives you get
\[y^3+3xy^2y'+y+xy'=0\]

Answer 3

replace \(x\) by \(10\) and \(y\) by \(1\) and solve for \(y'\)