The Differentials: Example 2

Problem:

Find dy if y=\frac{2x}{3x-1}.

Solution:

We get the differential of both sides of the equation.

dy=d\left(\frac{2x}{3x-1}\right)

We apply the different differential formulas

dy=\frac{\left(3x-1\right)\:d\left(2x\right)-2x\:d\left(3x-1\right)}{\left(3x-1\right)^2}

dy=\frac{\left(3x-1\right)\:\left(2\:dx\right)-2x\:\left(3\:dx\right)}{\left(3x-1\right)^2}

dy=\frac{\left(6x-2\right)dx-6x\left(dx\right)}{\left(3x-1\right)^2}

dy=\frac{\left(6x-2-6x\right)dx}{\left(3x-1\right)^2}

dy=\frac{-2\:dx}{\left(3x-1\right)^2}