Calculus 09

Calculus

Lesson 09 Chain Rule

Next, is there an easier way to deal with something like :

We could either multiply it out and then take the derivative:

Or, we could separate and use the Product Rule:

Or, we can use something new called the Chain Rule: we treat the

parentheses as we would if it were x, and then we multiply by the derivative

of what is actually IN the parentheses:

The technical way to say this is that we say ,

and then the chain rule says:

So we say:

More Examples:

Also note:

On to Lesson 10 - Implicit Differentiation