partial derivative chain rule


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Long chain rule
illustration of long chain rule Longest chain consisting of six carbon atoms..
Naming the side chains (or substituent)
If there is any other substituent on the chain, the compound is named as the derivative of the corresponding alkene. The side chains (or substituents) are named as per rules for alkane..
Food Chains
food chain system in the environment Food Chains - A food chain is a series of steps by which energy is obtained, used, and transformed by living things. For example; sunlight helps plants to grow, the plants are eaten by cattle, and lions eat the cattle. All living organisms of the biosphere are related to each ot..
Larger number of side-chains rule
If two different chains of equal lengths (equal number of C atoms) are possible, then select the chain which has larger number of side-chains i.e., select the more-branched chain. For example, in the following molecule, there could be two continuous cha..
Derivative of a Function of a Function
The differentiation of function of a function is known as 'chain rule'. The chain rule is probably the most widely used differentiation rule in mathematics. If y is a differentiable function of u and u is a differentiable function of x, ..
Derivative of a Function of a Function
So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we differentiate a function of a function? That is how can we differentiate sin (x 3 - 5)?So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we differentiate a function of a function? Th..
Working Rule for Finding Extremum Values Using First Derivative Test
Let f (x) be the real valued differentiable functio..
Carboxylic Acids and its Derivatives - Introduction
Carbon compounds containing a carboxyl functional group -COOH are called carboxylic acids. A carboxyl group is constituted of two groups - a carbonyl group and a hydroxyl group -OH. Carboxylic acids may be aliphatic (R-COOH) or aromatic (Ar-COOH) depending on whether -COOH group is attached..
Carboxylic Acids and its Derivatives - Introduction
functional formula of carbonyl group Carbon compounds containing a carboxyl functional group -COOH are called carboxylic acids. A carboxyl group is constituted of two groups - a carbonyl group and a hydroxyl group -OH. Carboxylic acids may be aliphatic (R-COOH) or aromatic (Ar-COOH) depending on whether -COOH group is attached to..
Lowest number rule
lowest number rule illustration When only one side chain is present: The carbon atoms in the selected parent chain are numbered as 1, 2, 3... from one end to the other. The numbering is done in such a way that the carbon atom carrying the side-chain is given the lowest possible number. For example, ..
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