Chapter 3 - The Derivative In Graphing And Applications - 3.1 Analysis Of Functions I: Increase, Decrease, and Concavity - Exercises Set 3.1 - Page 194: 6

$\frac{dx}{dy}$=$\frac{10xy-3x^{2} y^{2}-1}{2x^{3}y-5x^{2}}$

$\frac{d}{dx}(1) =\frac{d}{dx}(x^{3}y^{2} - 5x^{2}y+x)$ $x^{3}2y\frac{dy}{dx}+3x^{2}y^{2}-5x^{2}\frac{dy}{dx}-10xy+1=0$ $(2x^{3}y-5x^{2}\frac{dy}{dx})=10xy-3x^{2}y^2-1$ $\frac{dx}{dy}=\frac{10xy-3x^{2} y^{2}-1}{2x^{3}y-5x^{2}}$