No, there does not. By Darboux's theorem derivatives have the intermediate value property, and it's a common fact that an injective function on an interval that has the intermediate value property is continuous (cf. here for example)
No, there does not. By Darboux's theorem derivatives have the intermediate value property, and it's a common fact that an injective function on an interval that has the intermediate value property is continuous (cf. here for example)