C3 Differentiation

The Chain Rule

Example:

1- Bring the power to the front:

2- Take 1 away from remaining power:

3- Differentiate between the brackets:

4- Multiply this answer the the number in front of the brackets:

5- Answer:

Special Case

This is when it is X= instead of Y.

Example:

1 - Differentiate:

2 - Put 1 over:

3 - Simplify further if neccersary:

4 - Answer:

Product Rule

Example: 

1 - Choose your U and V values:

2 -  Differentiate these both: 

3 - Substitute these values into the formula:

4 - Pull out the common factors:

5 -  Simplify further if neccersary:

6 -  Answer:

Quotient Rule

Example:

1 - Write down your u and v values:

2 - Differentiate these values:

3 -  Substitute into the following formula:

4 - Pull out common factors:

5 - Simplify further if neccersary:

6 - Answer: