Further Differentiation and Integration f ’(x) x

Further Differentiation and Integration

f ’(x) x

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

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

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.

Another Approach

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.

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