How Can Mathematica Extract and Reuse Output Values for Further Computations?

[Orion1]

$$\text{In}[1]:=\text{Solve}\left[\partial _{\theta } \text{Sin}[\theta ]==0,\theta \right]$$

$$\text{Out}[1]:=\left\{\left\{\theta \to -\frac{\pi }{2}\right\},\left\{\theta \to \frac{\pi }{2}\right\}\right\}$$

Is there a Mathematica source code command that can read a specific numerical value from the output box data?

$$y_1[\text{x\_}]\text{:=}x^2$$
$$y_2[\text{x\_}]\text{:=}\partial_x x^2$$
$$\text{Plot}\left[y_1[x],\{x,0,1\}\right]$$
$$\text{Plot}\left[y_2[x],\{x,0,1\}\right]$$

ivar: ... is not a valid variable.

Is there a symbolic source code solution that will alloy me to define and plot a recently differentiated function?

I can plot the function by manually copying the output box data in immediate mode and pasting it back into the function definition.

 

[Dale]

$$y_2[\text{x\_}]\text{:=}\partial_x x^2$$
...
Is there a symbolic source code solution that will alloy me to define and plot a recently differentiated function?

Try:
$$y_2[\text{x\_}]\text{:=Evaluate[}\partial_x x^2\text{]}$$