Grab a white board and try the Starter – Question 1

Starter – Question 2 (c)

(c)

Differentiating Using The Quotient Rule A2 Maths

The Quotient Rule Aims: To be able to apply the quotient rule in order to differentiate y=f(x)/g(x) To successfully answer exam questions using the chain, product and quotient rules.

Bilborough College Maths - Core 3 differentiation: the product rule (Adrian) 05/05/2018 Quotient rule If Then “The derivative of the top times the bottom, minus the derivative of the bottom times the top, divided by the bottom function squared.”

The rule can also be written using function Bilborough College Maths - Core 3 differentiation: the product rule (Adrian) 05/05/2018 Quotient rule The rule can also be written using function Given The derivative is

Example 1 Differentiate y = Let u = 1+x2 and v = 1+ex Bilborough College Maths - Core 3 differentiation: the product rule (Adrian) 05/05/2018 Example 1 Differentiate y = Let u = 1+x2 and v = 1+ex Then differentiate each one Finally apply the rule ……………

Bilborough College Maths - Core 3 differentiation: the product rule (Adrian) 05/05/2018 Example 1 (cont’d)

Example 2 Differentiate to find . Solution: and We now need to simplify.

Now collect like terms: Example 2 (cont’d) We could simplify the numerator by taking out the common factor x, but it’s easier to multiply out the brackets. We don’t touch the denominator. Now collect like terms: and factorise: We leave the brackets in the denominator. ( A factorised form is considered to be simpler. ) Multiplying out numerator:

Quotients can always be turned into products. e.g. can be written as However, differentiation is usually more awkward if we do this. In the quotient above, and ( both simple functions ) In the product , and ( v needs the chain rule )

TARSIA TIME!!

Bilborough College maths - core 3 quotient rule (Adrian) 05/05/2018 Exercise Use the quotient rule, where appropriate, to differentiate the following. Try to simplify your answers: 1. 2. 3.

Bilborough College maths - core 3 quotient rule (Adrian) 05/05/2018 1. Solution: and

Bilborough College maths - core 3 quotient rule (Adrian) 05/05/2018 2. Solution: and

Bilborough College maths - core 3 quotient rule (Adrian) 05/05/2018 3. Solution: Divide out:

SUMMARY To differentiate a quotient: Check if it is possible to divide out. If so, do it and differentiate each term. Otherwise use the quotient rule: If , where u and v are both functions of x

Core 3 textbook Page 97 Exercise D Independent Study Core 3 textbook Page 97 Exercise D DUE: NEXT LESSON!