Question

If 5 xy = xy2 + 16 arctan(x) the tangent line at point (1, 1) has a slope approximately equal to:

Answer 1

implicit diff?

Answer 2

take the derivative of both sides wrt \(x\) and get
\[5y+5xy'=y^2+2xyy'+\frac{16}{1+x^2}\] replace \(x, y\) by 1 and solve for \(y'\)