Answer
$dx/dy=\frac{x(secy)^2-secx}{ysecxtanx-tany}$
Work Step by Step
Take the derivative as is on either side of the equation:
$ysecxtanx(dx/dy)+secx=x(secy)^2+(dx/dy)tany$
Move all terms with dx/dy onto one side of the equal sign and distribute the dx/dy out of each term:
$dx/dy(ysecxtanx-tany)=x(secy)^2-secx$
Isolate dx/dy by dividing both sides by the terms:
$dx/dy=\frac{x(secy)^2-secx}{ysecxtanx-tany}$