Just like when you learned limits, you had to start by learning how to read the notation. The same is true with derivatives.
As with a lot of things in math, there a bunch of ways to say the exact same thing. Here is some of the notation you will see when talking about derivatives. This is not an exhaustive list, but covers the majority of notation you will run across.
Type of Notation |
Prime Notation: Named because you use little prime tic marks. |
Differential Notation: Named for its use of what are known as differentials (dx, dy, dt) |
Directions you will see that tell you to find the derivative. |
With prime notation it will normally be in the language. “Differentiate ” |
Differential notation uses notation to say everything.
The top of the notation is saying take the derivative of this equation, and the bottom is saying with respect to x (this is the variable you care about).
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First Derivative Taking the derivative once. |
Read “f prime of x” |
Read: “d…y…d…x” Or “derivative of y with respect to x”
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Second Derivative Taking the derivative twice. |
Read “f double prime of x” |
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Higher Order Derivative Take the derivative as many times as they want you to. 3 times, 100 times, n-times |
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Find the derivative at x = 3 . |
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Find the slope of the tangent line at x = 3 . |
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