Difference between revisions of "Derivative"

Revision as of 23:07, 9 September 2006

The derivative of a function is defined as the instantaneous rate of change of the function with respect to one of the variables. Note that not every function has a derivative.

The following pages provide additional information on derivatives.

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 The '''derivative''' of a [[function]] is defined as the instantaneous [[rate]] of change of the function with respect to one of the [[variable]]s.  Note that not every function has a derivative.
-== Notation ==
-The derivative of f(x) can be expressed in several ways including:
-* <math>\frac{d}{dx}</math>
-* <math>\displaystyle f'(x)</math>
-* <math>\displaystyle f'</math>
-== Finding the Derivative ==
-For any constant, the derivative is 0.
-For any monomial <math>nx</math>, the derivative is n.
-Note that when we take the derivative of any polynomial <math>\displaystyle a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0</math>, we can take the derivative of each addend and then add these to find the derivative of the polynomial.
-The [[chain rule]] states that the derivative of any <math>\displaystyle ax^n</math> is <math>\displaystyle anx^{n-1}</math>
-To find the derivative of <math>\displaystyle f(x) \cdot g(x)</math> we cannot do what we did with addition.  We must instead use the [[product rule]]: <math>\displaystyle (f \cdot g)' = f'g + g'f</math>
-The [[quotient rule]] states that <math>\displaystyle (\frac{f}{g})' = \frac{f'g - fg'}{g^2}</math>
 The following pages provide additional information on derivatives.

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Difference between revisions of "Derivative"

Revision as of 23:07, 9 September 2006

See also