Differentiable function impleis uniform convergence

Question

If $f_n$ is differentiable, does that imply $f_n \to f$ uniformly if $f$ is the limit of $f_n$?

If so, is it a good idea to use the formal definition of differentiability, then show from this that $f_n$ satisfies the definition of uniform convergence?

Please help me with this.

Answer 1

The sequence $f_n(x)=x^n$ in $[0,1]$ is a counterexample.