Aims: To be able to differentiate using the various methods needed for C3.

Session Outcomes  Use Chain Rule to differentiate the various composite functions required by C3.  Use the product rule to differentiate the product of two functions.  Use the quotient rule to differentiate a function over another.

Some standard rules…

Chain Rule…  The chain rule is a versatile method that is used to differentiate compositions of functions.  It is based upon this idea… If y is a function performed on u where u itself is a function of x then the derivative of y in terms will be the product of the derivative of the y function on the function u multiplied by the derivative of u in terms of x.

Fully Worked Example…

To try…

Patterns  The Chain Rule tends to create patterns. To differentiate function g performed on f(x)… f(x) is u The result is the derivative of the inner function multiplied by the derivative of the outer performed on the inner.

Eh??? Useful Rules

Product Rule  The Product Rule is a method to differentiate the product of two functions…  It is often written as… If y is the product of two functions of x (named u and v) the derivative of y is the sum of the product of each individual function and the derivative of the other.

Example Can often require use of chain rule

Try These

Stationary Points  The process of factorising answers to simplify can be useful in finding stationary points.

Quotient Rule  The quotient rule is essentially an adaptation and simplification of the product rule it states… If y is function u over function v (where u and v are functions of x) then the derivative of y can be found by subtracting the derivative of the denominator multiplied by the numerator from the derivative of the numerator multiplied by the denominator then dividing this difference by v squared.

Try Some

Example

Stationary Points  When using quotient rule we usually end up with another quotient In division the only way to equate to 0 is to have a numerator of 0.

Whichity Way?

Examination Style Stuff