Question on derivative

I have this :

And i don't understand (3.5) .

i.e : why $\displaystyle\frac{d}{dt} G_t(\eta(t)u)=(G'_t(\eta),\eta ')+\partial_tG_t(\eta))$

Please Thank you .

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I would guess that it's some kind of functional chain rule, but I don't quite see it. Look in the rest of the book/article to see if they use a similar device with possibly more explanation. – icurays1 Jun 17 '13 at 17:16
there is not more – Vrouvrou Jun 17 '13 at 17:22