- #1

Dragonfall

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- 4

## Homework Statement

For [tex]f\in C([0,1])[/tex], let [tex]N(f)=\int_0^1(f(t))^2dt[/tex]. Show that [tex]N\in C^{\infty}[/tex] and calculate the first derivative.

## Homework Equations

Can I use Leibniz's integral rule for this?

## The Attempt at a Solution

If I just blindly plug in the formula, I get

[tex]dN/df=\int_0^12f(t)dt[/tex]