1. Differentiation
Revision for IB SL

2. Rule used to differentiate
Type of function
Rule used to differentiate
Polynomial
Constant
Always becomes zero
Remember that , e , ln(3), are still constants
Composite function (function of a function)
Chain rule

3. Rule used to differentiate
Type of function
Rule used to differentiate
2 functions of x multiplied together
Product rule
1 function of x divided by another function of x
Quotient rule
Exponential function

4. Rule used to differentiate
Type of function
Rule used to differentiate
Natural logarithm
Trigonometric functions

5. Chain Rule

6. Product Rule

7. Quotient Rule

8. ex

9. ln(x)

10. Trigonometric functions

11. Find gradient at particular point
Substitute the x-value for that point into the expression for dy/dx.
With implicit functions, you will need the x and y values.

12. Find tangent or normal
A tangent or normal is a straight line (y = mx + c).
For the tangent, m is the gradient at that point.
For the normal, m is

13. Find turning points and their nature (min/max)
Turning pt is when dy/dx=0
To determine nature:
Use 2nd derivative test If d2y/dx2:
> 0, local minimum
< 0, local maximum
= 0, test inconclusive – could be min, max or point of inflection
Examine gradient on either side of the point. Use this method if finding the 2nd derivative is too hard or if the test was inconclusive.

14. Find turning points and their nature (min/max)

15. Points of inflection
A point of inflection is the point on a curve when it changes from concave-up to concave-down, or vice-versa.
This is the point when the second derivative, d2y/dx2, equals zero

16. Summary

17. Motion of particles s, displacement v, velocity a, acceleration
E.g. what is the velocity function for a particle if its displacement function is
s = (3x-2)4
Differentiate