Discontinuous derivative of a differentiable plane curve
= Discontinuous derivative of a differentiable plane curve
{title2=$f(t)=t^2(\sin(1/t),\cos(1/t))$}
Set $f(0)=0$. The difference quotient has <Euclidean norm> $|t|$, so $f'(0)=0$. For $t\ne0$, differentiation gives $\|f'(t)\|^2=1+4t^2$. Thus this <differentiable> curve has a <derivative> discontinuous at zero, despite each scalar component satisfying the usual one-dimensional derivative properties.