Hello PH, This is my first post. I came here while studying partial derivatives and after clicking here and there for over 4hrs for an answer. While practicing the derivatives rules i came across the hideous quotient rule. I've solved around 20 fractional problems trying to find a decision tree that will help me understand why and when to use (or not to use) the quotient rule. I have no problem in rewriting the function to another one with a negative exponent in the numerator and use the product/chain/power rule when necessary. So, is it possible to precisely know when to avoid the quotient rule?