Answer
$\frac{dp}{dq}=\frac{6q-4p}{3p^2+4q}$
Work Step by Step
Take the derivative of the equation on each side separately. Apply chain rule when differentiating the "p" variables since we are differentiating with respect to q:
$3p^2\frac{dp}{dq}+4p(1)+4q\frac{dp}{dq}-6q=0$
Move all terms with dy/dx to one side of the equation, and isolate dp/dq:
$3p^2\frac{dp}{dq}+4q\frac{dp}{dq}=6q-4p$
$\frac{dp}{dq}(3p^2+4q)=6q-4p$
$\frac{dp}{dq}=\frac{6q-4p}{3p^2+4q}$
