differentiation - Derivative of delta function

I am reading and following along the appendices of "The Physical Principles Of The Quantum Theory", and trying to learn how he derives Schrödinger's Equation from his Matrix Mechanics, but I have run into a bit of trouble. It seems like for his derivation to work, it must be necessary for the integral of a function times the Dirac Delta Function's derivative be: $$\int^{\infty}_{-\infty}f(\xi)\delta'(a-\xi)d\xi=f'(a). \tag{36}$$ But the actual identity is $$\int^{\infty}_{-\infty}f(\xi)\delta'(\xi-a)d\xi=-f'(a).$$ Does anybody care to explain why it is like this in Heisenberg's book, or provide a derivation along the same vein, but with the correct identity for the delta function?