1. Further Differentiation and Integration
f ’(x) x

2. Further Differentiation and Integration

3. f ’(x) x

5. For these results to be true, x must be measured in radians.

6. Integrating Sin x and Cos x
Since and
For these results to be true, x must be measured in radians.

8. Derivative of (ax + b)n Taking this a step further:
This is known as the chain rule.
My rule:- Differentiate outside, differentiate inside then multiply.

10. Another Approach

12. Applications
The chain rule allows us to investigate applications involving composite functions.
Remember: to find the equation of a line we need a point and a gradient.

14. Integrating (ax+b)n Here we can use the chain rule. + C 5 × 3
My rule: Integrate outside, differentiate inside then divide.
+ C 3
× 2