The Quotient Rule
If f and g are differentiable at x
and 
The quotient rule states:
| The Quotient Rule If f and g are differentiable at x
and
|
By the definition of the derivative
By the definition of the derivative
g is differentiable at x and therefore continuous at x.
Hence
The limit of a constant is the value of the constant. As there is no h
in g(x), we can treat g(x) as a constant
when finding its limit as h tends to zero. So
Using each of the above facts we then obtain:
which is the quotient rule.