Partial derivatives are just ordinary derivatives… with everything else temporarily frozen.
When you have a surface z = f(x,y), taking a partial derivative with respect to x means: freeze y, slice the surface in the x-direction, and look at the slope of the curve you get. As you move the slice across the surface, those tangent slopes change, and that changing slope is exactly what the partial derivative describes.
I built an interactive graph so you can actually see this happen instead of just memorizing the notation. Click the image below, and notice how the tangent lines change their slope. Once you see partial derivatives this way, the notation becomes much more intuitive.
That’s it. One idea in under a minute.
— DIBEOS
P.S. If you want to learn more about differentiation in multivariable calculus, click here:
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