1. Differentiation and integration part 1
Differentiating trig functions
Gradient for parametric equations
Gradient for a curve given implicitly
Forming Differential equations
Integrating

2. Differentiating trig functions
You need to know

3. 1. Differentiate
Write

4. 2.Differentiate Set out equations on the right of the page
Differentiate each – take care with the names of the derivatives
Combine
Simplify

5. Example 3 A curve is given by
(a)Find in terms of θ. Find the equation of the tangent to the curve at the point where the parameter takes the value

6. Example 3
The curve is given by

7. Implicit differentiation
We use a version of the chain rule to help us to differentiate when the equation cannot easily be rewritten as y = ….
This means we differentiate with the wrong letter and correct it by multiplying by dy/dx

8. Implicit Example 4
Differentiate the whole equation wrt x
Rearrange

9. 5.Implicit differentiation
Find the stationary points on the curve given by
Differentiate whole equation wrt x
Collect terms and simplify
Product rule needed for this term

10. Forming differential equations
Newton’s law of cooling states that the rate of cooling of a body is proportional to the excess temperature Using write this as a differential equation.
The minus indicates decrease in temperature
The dt derivative is always the rate of ….
Excess temperature
The k converts “proportional to” into an equation

11. Which of the functions on the table are of this type?
Integrals of the form
Once you recognise the fraction as being of this type, you can just write down the answer.
Which of the functions on the table are of this type?