Past exam of the mathematical methods II course of the University of Oxford / 2013 / 1

Work where $x\ne 0$ and $f$ is differentiable. Set $q=y/x$. The chain rule givesConsequentlyGeometrically, a radial rescaling of both coordinates leaves $y/x$ unchanged, so the function has zero rate of change along radial dilations. No value or derivative at $x=0$ is implied by this representation.