proof of quotient rule (using product rule)

Suppose f and g are differentiable functions defined on some interval of , and g never vanishes. Let us prove that


Using the product ruleMathworldPlanetmath (fg)=fg+fg, and (g-1)=-g-2g, we have

(fg) = (fg-1)
= fg-1+f(g-1)
= fg-1+f(-1)g-2g
= fg-fgg2
= fg-fgg2.

Here g-1=1/g and g-2=1/g2.

Title proof of quotient rule (using product rule)
Canonical name ProofOfQuotientRuleusingProductRule
Date of creation 2013-03-22 15:00:45
Last modified on 2013-03-22 15:00:45
Owner matte (1858)
Last modified by matte (1858)
Numerical id 5
Author matte (1858)
Entry type Proof
Classification msc 26A06