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Unformatted text preview: Differentiation Revision
Remember that the derivative of a function is simply the instantaneous rate of change of that function. = + − = sin cos tan cos −sin sec ln 1 The Scooter Tutor www.thescootertutor.com.au The Rules: Product Rule – For use when you need to find the derivative of a function that is the product (multiple) of two individual functions: = × . It states that the derivative of such function can be calculated by: = Example: = Steps: 1. Establish functions: = =2 and and then take the derivative of those two sin × + × ′ = sin = cos = × + × 2. Now we apply our results to the formula: = 2 sin + cos And that is the final answer. The Scooter Tutor www.thescootertutor.com.au Quotient Rule – For use when you need to find the derivative of a function divided by another function. i.e. when = It says that the derivative of these functions is given by: = Example: = Steps: 1. Define = =2 and : = sin = cos =
× × × − × sin ′ 2. Substitute the values into the formula: = 2 sin − sin cos And that is the final answer. The Scooter Tutor www.thescootertutor.com.au Chain Rule – For use when the function we are trying to derive contains a function of a function. i.e. = The chain rule states that the derivative of the sort of function is given by: = Example: = sin 1. The first step is to determine our external and internal functions: = sin = 2. Now, take the derivative of these two functions = cos =2 3. Then substitute our derivatives into the rule: = 2 cos 4. And finally we need to replace the which was . = 2 cos with the original value for × The Scooter Tutor www.thescootertutor.com.au The Rules: A Summary Name Product Rule Quotient Rule Chain Rule =
= ∙ Rule + ∙
− Use ∙
∙ Example = = ln 4 −2 tan = ∙ Function times function Function Divided by function Function of function = sin cos When you are working with these rules be sure that you don’t limit yourself to using only one of them. Many questions demand that you use two or more. For example = uses all of the rules above. Give it a try and email us if you get stuck. I hope this document helps you prepare for your exams and if there is anything you would like added, or if there are any mistakes, please let us know at: Info@thescootertutor.com.au If you’re finding Maths tough, we are always available for one-on-one tutoring. Good Luck, The Scooter Tutor www.thescootertutor.com.au The Scooter Tutor www.thescootertutor.com.au ...
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- Spring '10