Continuing this process, we can continue to remove layers of complexityįrom the function until we arrive at elementary expressions that we know how toĭifferentiate. □ ( □ ), but this too can be broken down into smaller This ofĬourse means that we need to find the derivative of In other words, □ ( □ ) is a composition ofįunctions, so we can apply the chain rule to help us differentiate it. □ ( □ ) separately in this way, we can see that Separately and add them together afterwards. Using the linearity of differentiation, this means we can differentiate If we do this, we can see that it is the sum Generally, the best way to do this is to begin by considering the outermost Īt first, this may seem impossible to deal with, but we can break it into parts. Many different operations together, and how we can tackle the differentiation by Let us consider an example of differentiating a complicated function combining Will look at a number of examples that will highlight the skills we need Simplifications that will make the process easier. Trivial exercise and it can be challenging to identify the correct rules toĪpply, the best order to apply them, and whether there are algebraic However, we should be aware that this is often not a In addition to using these rules separately, it is also possible to use them inĬonjunction with each other, allowing us to differentiate any combination ofĮlementary functions. differentiation of the integration is equal to the value of the function or vice versa.For differentiable functions □ ( □ ) andĪnd constants □, □ ∈ ℝ, we have the following rules: Differentiation is the opposite of integration i.e. A differentiable function may be defined as is a function whose derivative exists at every point in its range of domain. We should remember that a differentiable function is always continuous but the converse is not true which means a function may be continuous but not always differentiable. Hence the main difference between the chain rule and product rule is that it is used for the differentiation of the function of a function and the other is used for the differentiation of the product of the function. when the function is to be differentiated is in the form of \. Therefore, we getĬhain rule is a rule which is used to differentiate the composition of the functions i.e. We will write the basic definitions of the chain rule and product rule. In order to find derivatives of a function, we generally use the product rule first and then the chain rule. Both rules are used in the method of differentiation. Then by using these definitions, we will get the difference between the chain rule and product rule. Hint: Here we will write the definition of the chain rule and the product rule with example.
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