In conclusion, use the quotient rule to help you find the derivative of functions that have fraction expressions in them, but only if you have to. It often gives you and ugly expression that is difficult to simplify and may steer you towards an incorrect answer if you use it when there are easier methods.n order to differentiate this, we need the product rule. The product rule allows us to differentiate a function when the function is a product of two distinct parts. In this example, we have the polynomial 3x 2 + 4x - 5 and the transcendental function sin(x).
1 All carbohydrates are characterized by the carbonyl functional group (C=O) along with a number of hydroxyl functional groups(CâOH). 2  Aldehydes have the carbonyl group at the end of the molecule. 3  Glucose, pictured here, is an example of an aldehyde sugar (aldose). 4  It is the most common monosaccharide in living systems. All carbohydrates are characterized by the carbonyl functional group (C=O) along with a number of hydroxyl functional groups(CâOH). 2  Aldehydes have the carbonyl group at the end of the molecule. 3  Glucose, pictured here, is an example of an aldehyde sugar (aldose). 4  It is the most common monosaccharide in living systems.
deoxyribose sugars, which are bonded to a phosphate group and a nitrogenous base. Very useful little critters, they are basically a nitrogenous base, a five-carbon sugar, and one to three phosphate groups (mono-to tri-phosphate).