To find the equation for a normal line using differentiation, just follow these simple steps:

1. Identify the function: Start by picking the function you are working with. Let’s call it $f(x)$. You will find the normal line at a specific point, which we'll call $(a, f(a))$.

2. Calculate the derivative: Next, find the derivative of the function, written as $f'(x)$. This tells you the slope of the tangent line at any point $x$ on the curve.

3. Determine the slope of the normal line: The slope of the normal line is different from the tangent slope. It is the negative reciprocal of the tangent slope. So, if the tangent slope at $x = a$ is $m = f'(a)$, then the slope of the normal line is:

   $$m_{normal} = -\frac{1}{m} = -\frac{1}{f'(a)}$$

4. Use point-slope form: You can write the equation of the normal line using something called point-slope form. It looks like this:

   $$y - f(a) = m_{normal}(x - a)$$

   If you put in $m_{normal}$, you get:

   $$y - f(a) = -\frac{1}{f'(a)}(x - a)$$

5. Simplify: Finally, you can rearrange the equation to get it into a simpler form, like the slope-intercept form, which is $y = mx + b$ if you want.

By following these steps, you can easily find normal lines for any differentiable function at specific points!