Step 1:

We notice that the given function is a composite function, or a function within another function. To find the derivative of composite functions, we will use the chain rule. We can see that the inner function is [latex]1-x^2[/latex] and the outer function is the the exponential function.

The chain rule states:

[latex]\Large{\frac{d}{dx}f(g(x)) = f'(g(x)) \cdot g'(x)}[/latex]

Step 2:

Applying the chain rule, we have:

[latex]\Large{\frac{d}{dx}(e^{1-x^2})}[/latex]

[latex]\Large{= e^{1-x^2} \cdot \frac{d}{dx}(1-x^2)}[/latex]

Step 3:

Simplifying, we have:

[latex]\Large{ = -2xe^{1-x^2}}[/latex]

Thus, this is the final answer for the derivative. So:

[latex]\Large{f'(x) = -2xe^{1-x^2}}[/latex]

Solution Complete!