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]
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ivar: ... is not a valid variable.
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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.
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[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{]}