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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 : Trigonometric functions:

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  • 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): [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 : Trigonometric functions:
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abstract
  • 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 : * [Proof] * [Proof] * * (Product rule) * * (Quotient rule) * (Chain rule) Trigonometric functions: * [Proof] * * * * * * * * * * * Logarithmic and exponential functions: * * * [Proof] *
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