Derivative Review - California State University, Sacramento



Derivative Review

Derivative shows the rate of change and it is represented as [pic] which reads rate of change of Y with respect to X. Since constant cannot change, then the derivative of a constant is zero. In general, if [pic][pic]. For instance, [pic]or [pic]

Note that we also use f’(x) to mean derivative of f(x) with respect to x.

Rule #1:

Derivative of [pic]

Rule #2:

If [pic]then

derivative of h(x) with respect to x is:

[pic]

Rule #3:

If [pic] and [pic] the derivative of y with respect to x is:

[pic]

Example #1:

Find the derivative of [pic]

Using Rule #1: [pic]

and [pic]

[pic]

Example #2:

Find the derivative of [pic]

Using Rule #2,

[pic]

Example #3:

Find the derivative of [pic].

Using Rule #3, let’s define [pic]

Then [pic]

[pic]

[pic]

Example #4:

Find derivative of [pic]

[pic]let [pic]

[pic]

[pic]

Example #5:

Find the derivative of [pic].

First define [pic]or[pic]

[pic]

[pic]

[pic]

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