# Derivative formulas

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The derivative of any polynomial function of one variable is easily obtained. If (or a constant function) and are both differentiable on some set , then so are , , , and . If, in addition, is nonzero on , then (and also ) are differentiable on . Also, if is differentiable on , then is differentiable on . For the trivial case of , for some constant (a degree 0 polynomial):

For any real-valued differentiable functions and :

- [Proof]
- [Proof]
- (Linearity)
- (Product rule)
- (Quotient rule)
- (Chain rule)

And for any real number *r*:

Which covers any single variable polynomial function. Derivatives of non-polynomial functions require additional rules.