A derivative of a function is a second function showing the rate of change of the dependent variable compared to the independent variable. It can be thought of as a graph of the slope of the function from which it is derived. The process of finding a derivative is called differentiation.
Definition |
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Let and be a function. Then the derivative of is a function defined by:
The derivative is undefined when this limit does not exist, that is, is not differentiable. |
Properties
- See also: Derivative formulas
A simpler way of finding the derivative is to multiply the coefficient by the exponent and subtract one from the exponent (proof). For example:
The function
can be differentiated as follows:
In graphs, the derivative of a function at a number is equal to the slope of the tangent line of the graph of at the point .