Shortcuts for Derivatives

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Presentation transcript:

Shortcuts for Derivatives Objectives -learn and apply the constant rule -learn and apply the power rule

Why are the rules helpful? If you had to use the limit definition to find the derivative of the following, it would be quite complicated.

Constant Rule f’(x)=0 (constant rule) f(x)=c is a constant function in which the graph is a horizontal line which has a slope of 0. Therefore, if f(x)=c f’(x)=0 (constant rule) Example- f(x)=5 f’(x)=0

A derivative is nothing more than the rate of change of a function at a particular point. Since it is a rate of change, it makes sense that the derivative gives us a slope of a tangent line. Therefore it also makes sense that the derivative of a constant function is 0, since there is no rate of change on a horizontal line.

Power Rule If then Simply put, to use the power rule there are 2 steps Bring down the power on the variable. Drop the power by 1.

Examples 1) 2) 3)

Another Example

Application Find the equation of the tangent line to

Homework Power Rule WS