Help with derivation step in Kepler orbit, using chain rule Picture of equations
Hello, I am trying to work out the derivation of the Kepler orbit myself with help of the following wiki article, link: 
In the picture above, I'm unsure how differentiating equation 5 with respect to $t$ produces equation 6. I tried using product rule:
$$\frac{d}{dt}\left(\frac{dr}{dt}\right)=\frac{d}{dt}\left(\frac{dr}{dθ}\cdot\frac{dθ}{dt}\right)$$
$$\frac{d^2r}{dt^2}=\left(\frac{dr}{dθ}\right)'\frac{dθ}{dt}+\frac{dr}{dθ}\left(\frac{dθ}{dt}\right)'$$
$$\frac{d^2r}{dt^2}=\frac{d^2r}{dθ^2}\left(\frac{dθ}{dt}\right)^2+\frac{dr}{dθ}\frac{dθ}{dt^2}$$
Precisely, I don't understand how $\displaystyle{\left(\frac{dr}{dθ}\right)'\frac{dθ}{dt}}$ becomes $\displaystyle{\frac{d^2r}{dθ^2}\left(\frac{dθ}{dt}\right)^2}$.

By the Chain Rule
$$\frac{d}{dt}\left(\frac{dr}{d\theta}\right)=\frac{d\theta}{dt}\frac{d}{d\theta}\left(\frac{dr}{d\theta}\right).$$
