Derivatives
Product and Quotient Rules
If the equation contains two polynomials multiplied or divided then the derivative is best solved by the product rule or the quotient rule as described below.
Product rule: Say you have two functions f(x) and g(x). If they are multiplied together you would have the term f(x) * g(x). The rule for the derivative is as follows:
.
As easy way to say it to yourself is:
First times the derivative of the second plus second times the derivative of the first.
Quotient rule: Just like the product rule except divided. You would see
. The rule for the derivative is as follows:
An easy way to say it to yourself is:
Low D high minues high D low over low squared.(where low means the denominator, high means the numerator, d refers to “the derivative of” and the multiplications are implied)
For example:
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