FOC for King–Plosser–Rebelo preferences I am reading Dynamic scoring: A back-of-the-envelope guide by Mankiv and Weinzierl (here) and on page 1420, I don't get the FOC in equation $(10)$, which says $r=...$.
I do get the FOC with $v'(n)=...$ by using Lagrange. 

I found the same FOC in a paper from Ferede (Dynamic Scoring in the Ramsey Growth Model, here) and he says, that it 


  is obtained by combining the first order conditions of the utility
  maximization with respect to capital and consumption (page 5).


But I only observe $\lambda=-c^{-\gamma}e^{gt(1-\gamma)}e^{(1-\gamma)v(n)}$ from the FOC w.r.t. consumption and $-\lambda[(1-\tau_k)r-g]=0$ from the FOC w.r.t. capital. 

How am I supposed to get $\dot{n}$ and $\dot{c}$ there?

Well let me show you, what I have got: The Lagrange-function is given by: 

$$L=\frac{1}{1-\gamma}[c^{1-\gamma}e^{gt(1-\gamma}e^{(1-\gamma)v(n)}-1]-\lambda [(1-\tau_n)wn + (1-\tau_k)rk - c - gk +T - \dot{k}]$$ 

So the FOC w.r.t. consumption is given by $\frac{\partial L}{\partial c}=c^{-\gamma}e^{gt(1-\gamma)} e^{(1-\gamma)v(n)}+\lambda=0$, while the FOC w.r.t. to capital is $-\lambda[(1-\tau_k)r-g]=0$. 

So the equation for $\dot{\lambda}$ is based on the equation $\frac{\partial \lambda}{\partial t}=\frac{\partial \lambda}{\partial c} \frac{\partial c}{\partial t}$. And you are fully differentiating it.

I hope someone can help me.

NEW:
So again: $\lambda=e^{-pt}u'(c)$. So you are indeed right with your equation after your words "Then substitute back in the FOC for consumption", but then you substitute it to the FOC wrt to k: $\dot{\lambda}=\lambda[g-(1-\tau)r]$, so we get $\gamma \dot{c}/c - (1-\gamma)(g+v'(n)\dot{n})+p=g-(1-\tau)r$, so that the signs don't fit anymore and this unfortunately leads to something else than equation $(10)$.
So Lets use a present value Hamiltonian here:

$H=e^{-pt}u(c)+\lambda(\dot k)$

FOC:
wrt c: $0=e^{-pt}u'(c)-\lambda$

wrt k: $-\dot\lambda=\lambda[(1-\tau)r -g]$

Take the FOC from consumption and differentiate wrt to time:

$\dot\lambda =-\gamma c^{-\gamma-1}\dot c e^{-pt+gt(1-\gamma)}e^{(1-\gamma)v(n)}+c^{-\gamma}e^{-pt+ gt(1-\gamma)}e^{(1-\gamma)v(n)}[(1-\gamma)(g+v'(n)\dot n)-p]$

Then substitute back in the FOC for consumption:

$\dot\lambda =-\gamma c^{-1}\dot c\lambda +\lambda[(1-\gamma)(g+v'(n)\dot n)-p]$

Then substitute this guy into the Foc for capital:

$g-(1-\tau )r=-\dot c/c\gamma+(1-\gamma)[g+v'(n)\dot n]-p$

leading to: 

$r(1-\tau)=p+(\dot c/c +g)\gamma+(1-\gamma)[-v'(n)\dot n] $