# Relation Between Yield Curve, First Order Derivative of YC and Forward Rate

I'm reading the book, "Derivatives Analytics with Python" by Yves Hilpisch. In an application of calibration of CIR85 process for the short-term interest rate. I found some codes which can be interpreted as which follows. The forward rate = spot rate + first order derivative of spot yield curve w.r.t. time horizon * time horizon. The full python script can ben found in the following link, http://www.riskreversal.net/calibration-of-cir85-model-to-euribor-rates/, and the formula in question is located in line 35. Could anyone give some additional explanation about the logic of the formula or indicate some reference regarding the issue. Thanks a lot!

$$B(0,t)=e^{-y(0,t) \, t}=e^{-\int_0^t{f(0,u) \, du}}$$
$$y(0,t) \, t=\int_0^t{f(0,u) \, du}$$
$$y(0,t)+ y\prime (0,t) t=f(0,t)$$