Proof of the Quotient Rule Let F = f/g be the quotient of two functions that are different...

Proof of the Quotient Rule Let F = f/g be the quotient of two functions that are differentiable at x.

a. Use the definition of F′ to show that

b. Now add −f(x)g(x) + f(x)g(x) (which equals 0) to the numerator in the preceding limit to obtain

Use this limit to obtain the Quotient Rule,

c. Explain why f′ = (f/g)′ exists, whenever g(x) ≠ 0.