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

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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.

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Some standard rules…

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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.

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Fully Worked Example…

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To try…

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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.

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Eh??? Useful Rules

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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.

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Example Can often require use of chain rule

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Try These

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

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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.

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Try Some

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Example

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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.

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Whichity Way?

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Examination Style Stuff

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