Derive the Quotient Rule from the Product Rule as follows. a. Define the quotient to b...

Derive the Quotient Rule from the Product Rule as follows.

a. Define the quotient to be a single function,

b. Multiply both sides by g(x) to obtain the equation Q(x) · g(x) = f (x).

c. Differentiate each side, using the Product Rule on the left side.

d. Solve the resulting formula for the derivative .

e. Replace Q(x) by and show that the resulting formula for is the same as the Quotient Rule.

Note that in this derivation when we differentiated Q(x) we assumed that the derivative of the quotient exists, while in the derivation on page 123 we proved that the derivative exists.