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# 8.10: Derivatives of Sums and Differences

Difficulty Level: At Grade Created by: CK-12
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### Vocabulary Language: English

derivative

The derivative of a function is the slope of the line tangent to the function at a given point on the graph. Notations for derivative include $f'(x)$, $\frac{dy}{dx}$, $y'$, $\frac{df}{dx}$ and \frac{df(x)}{dx}.

differentiable

A differentiable function is a function that has a derivative that can be calculated.

product rule

In calculus, the product rule states that the derivative of the product of two functions equals the first function times the derivative of the second function, added to the second function times the derivative of the first function.

theorem

A theorem is a statement that can be proven true using postulates, definitions, and other theorems that have already been proven.

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