Derivatives
The formal definition of a derivative is
Stated simply, the derivative is an equation of a function that represents the slope of another line.
Here is an example of using the formal definition of the derivative to calculate the derivative of x to the second power.
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Start with the formal definition.
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Put f(x) into the formal definition.
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Simplify.
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Subtract x^2.
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Cancel out h.
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Evaluate the limit.
The final answer is 2x as you can see. Fortunately, the derivative can be found using a shortcut called the Power Rule.
Power Rule
The Power Rule is a shortcut for calculating the derivative of a term. Note: The notation d/dx will be used to signify "the derivative of". Here's the equation.
Therefore, the derivative of 3x^2 would be
Derivative Table