# The Quotient Rule

The Quotient Rule

If and are both differentiable at and , then the derivative of their quotient at is given by the quotient rule shown above. On the graph, is blue, is red, is purple, and the derivative of is thick purple.

f

g

x

g(x)≠0

x

f

g

f(x)/g(x)

f(x)/g(x)