1. While We Wait To Start Differentiate the following functions e x 8x 3 (9x-3) 5 Write the general chain rule

2. Starter Differentiation Card match Match expressions with derivatives

7. Differentiating e f(x) Aims: Be able to use the chain rule to differentiate functions of the form e f(x) Spot the pattern in the results so that functions of e f(x) form can be quickly differentiated.

8. Lesson Outcomes Describe: How you can use the chain rule to differentiate functions of the form y=e f(x) Explain: How there is a pattern that enables us to easily and quickly differentiate functions of this type.

9. Exercise: mini whiteboards Use the chain rule to differentiate the following: 1.2.

10. Exercise: mini whiteboards Use the chain rule to differentiate the following: 1.2.3.

11. Solutions 2. 3.

12. So, the chain rule says  differentiate the inner function  multiply by the derivative of the outer function e.g.

13. So, the chain rule says  differentiate the inner function  multiply by the derivative of the outer function ( The outer function is ) ( The inner function is ) e.g. With exponential functions, the index never changes.

14. Activity: Differentiating e ax+b Dominoes

15. Below are the exercises you have already done using the chain rule with exponential functions. 1.2.3. See if you can get the answers directly. Answers: 1. 2. 3. Notice how the indices never change. Make up some of your own and try them.

16. So, the chain rule says  differentiate the inner function  multiply by the derivative of the outer function ( The outer function is ) ( The inner function is ) e.g. With exponential functions, the index never changes.

17. plenary: Mini whiteboards try these