- #1

- 56

- 1

## Homework Statement

Prove the following

'()( − ) = −′()

∫

_{-∞}

^{∞}δ'(x)*f(x-a) = -f'(a)

## Homework Equations

∫

_{-∞}

^{∞}δ'(x-a)*f(x) = f(a)

## The Attempt at a Solution

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∫

_{-∞}

^{∞}δ'(x)*f(x-a) = ∫δ(x)*f(x-a)dx-∫f'(x-a)*δ(x)dx = f(-a) - f'(-a)

Went from 1st to second by integration by parts

Used integral definition of delta function to go to 3rd part