# Log differentiation of aggregate production function [closed]

Suppose we have an aggregate production function $$Y = A F(K, L)$$. I'm following some slides which then states that we if log differentiate we get the following: $$\frac{\dot{Y}}{Y} = \frac{\dot{A}}{A} + \frac{F_{K}' \dot{K}}{F K} + \frac{F_{L}' \dot{L}}{F L}$$. Where the dot notation $$\dot{Y}$$ is the differential of Y wrt. t. I've tried to using eulers theorem about homogen functions so that we can write $$Y = F_{k}'K + F_{L}'L$$, but I can't see where I would get the $$\frac{\dot{K}}{K}$$ terms.

EDIT: I wrote the formula wrong... its $$\frac{\dot{Y}}{Y} = \frac{\dot{A}}{A} + \frac{F_{K}' K \dot{K}}{F K} + \frac{F_{L}' L \dot{L}}{F L}$$
• This seems straightforward: have you tried differentiating w.r.t. $t$ and then dividing by $Y$? – Giskard Sep 3 '19 at 13:58
• In response to the edit: you can just simplify by $K$ and $L$. – Giskard Sep 3 '19 at 15:39