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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):

[Proof]

For any:

[Proof]

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

For any real-valued differentiable functions :

  • The definition of the derivative:

Basic derivative rules:

  • (Derived from Constant Multiple rule)
  • (Derived from Quotient rule)

Trigonometric functions:

Logarithmic and exponential functions:

  • [Proof]
  • [Proof]

Other:

[Proof]

[Proof]

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