I have got a task to calculate $\frac{dv}{dx}$ using backpropagation, where
$v = z^2 + y$
$z = \frac{y}{3}$
$y = \arctan(x)$
Am I supposed to just use chain rule here or do something else? I'd really like to see an example of calculating this.
I did something like this
$\frac{dv}{dz}$ = $2z$
$\frac{dz}{dy}$ = $\frac{1}{3}$
$\frac{∂v}{∂y}$ = $1$
$\frac{dv}{dy}$ = $\frac{∂v}{∂z}$$*$$\frac{dz}{dy}$ + $\frac{∂v}{∂y}$ = $\frac{2}{3}z$ $+1$
$\frac{dv}{dx}$ = $\frac{dv}{dy}$$*$$\frac{dy}{dx}$ = $(\frac{2}{3}z+1)*$ $\frac{1}{(1+x^2)}$