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Glissando

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## Homework Statement

If f(x) is an even function and f'(x) exists for all x, prove that f'(0) = 0. (Hint: Start with an equation that is true for all even functions and differentiate both sides with respect to x.)

## Homework Equations

Equation true for all even functions: f(x) = f(-x)

## The Attempt at a Solution

f(x) = f(-x)

f(d/dx (x)) = f(d/dx (-x))

f(1) = f(-1)

I'm not sure if I have the notation correct when differentiating...or I could have done something like this:

f(x) = f(-x)

f' (x) = f' (-x)

f'(0) = f'(-0)

Then I'm not too sure as to what to do from there ):

Thanks for all the help <3