CK12 Calculus - Single Variable

And a final way of expressingthe chainrule is the

easiestform to remember:Ifyis a functionofuanduis a functionofx, then

Example1:

Differentiate
Solution:

Usingthe chainrule, let Then

The exampleaboveis one of the mostcommontypesof compositefunctions.It is a powerfunctionof the
type

y= [u(x)]n.
The rule for differentiatingsuchfunctionsis calledtheGeneralPowerRule.It is a specialcaseof the Chain
Rule.

The GeneralPowerRule

if

then

In simplerform,if

then