A-level Mathematics/MEI/C3/Differentiation

Differentiation in Core 3 (C3) are an extension of the work that you did in Core 1 and Core 2.

Differentiation edit

Standard Derivatives edit

For the C3 module, there are a few standard results for differentiation that need to be learnt. These are:

 

 

 

 

 

Chain Rule edit

 

The Chain Rule is used to differentiate when one function is applied to another function. A typical example of this is:

 

One of the ways of remembering the chain rule is: Find the derivative outside, then multiply it by the derivative inside. In the example above, this becomes:

 

Product Rule edit

 

The product rule is used when two functions are multiplied together.

Quotient Rule edit

 

The quotient rule is used when one function is divided by another. It is a specific case of the product rule. A typical example of this is:

Implicit Differentiation edit

Implicit differentiation is used when a function is not a simple   but contains a mixture of x and y parts. A typical example of this is to differentiate:

 

When differentiating the y components of the expression you differentiate as normal, and then multiply by  . So differentiating both sides of the above expression it becomes:

 

Then by factorising the left hand side and cancelling, this becomes: