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Because the derivative is a limit, many of the rules of limits apply to the derivative:

- (
*cf*(*x*))' =*c*(*f'*(*x*)) where*c*is a constant. This says that the derivative of a scalar multiple of a function is equal to the derivative of the function multiplied by the scalar multiple. - (
*f*(*x*) +*g*(*x*)) =*f'*(*x*) +*g'*(*x*). The derivative of a sum of two functions is equal to the sum of the individual derivatives.

This is a powerful way of finding the derivative of a polynomial function. It says:

x^{n} = nx^{n-1} |

where *n* is a real number. For example,

x^{4} = 4x^{3} |

If *f* and *g* are two differentiable functions, then
(*fg*)' = *f'g* + *g'f*.
For example,

(3x)( = 3 +3x(x^{-}) |

If *f* and *g* are two differentiable functions, then

= |

For example,

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