NOTES ON CHAIN RULE OF DIFFERENTIATION

In order to understand the importance of chain rule in terms of differentiation, a method is to be followed. The formula, regarding computation of the derivatives, needs to be evaluated for understanding the importance of this attribute within the chain rule process. The composition of two or more functions can be considered as the outcomes of the chain rule process. In terms of defining the composite functions, chain rule differentiation is required. The differentiation formula can be considered as one of the most significant parts of the chain rule process. The relevant process with the help of which a derivative is found is often regarded as the derivative process. 

The concept of the chain rule

In physics, the chain rule is considered one of the most important attributes. There are some significant steps with the help of which, the chain rule is to be considered. 

• The first step is to identify the relevant inner function. Rewriting the outer functions by considering the replacement of the inner function can be considered important.
• Considering the derivatives regarding both of the functions is another and second most important step of the chain rule process. 
• The third step can be considered as the identification of the substitute regarding significant derivatives. In terms of considering the original expansion of the variables, this step is very important. 
• The next step can be considered as the simplification of the term and valuing the available attributes with efficiency.
• Multiplying the acquired results from the previous steps can be considered important.
• The last and another important step can be mentioned to simplify the derivatives of the chain rule.  

The importance of differentiation formulas

In order to solve problems within the chain rule process, the differentiation formula is found to be applied. The differentiation formula can be mentioned to be divided into four important rules. One of the most important rules is the power rule. The formula of power rule can be presented as (d/dx) (x^n ) = nx^{n-1}. Besides that, the sum rule can also be mentioned as another important rule of the differentiation formula. Formulas of product rule and quotient rule can be regarded as important also. In terms of mentioning the product rule formula, (d/dx) (fg)= fg’ + gf can be regarded as the appropriate one. On the other hand, the formula of the quotient rule is to be identified as (d/dx) (f/g) = [(gf’ – fg’)/g^2].   

Application of chain rule 

The chain rule is found to be applied in terms of finding the rate of changes within any function. At a certain time, the rate of change is found to be dependent on other significant functions. Such identified functions are considered to be nested on each other. The differentiation formulas are found to be used in terms of finding signification derivatives.

• One of the most important applications of chain rules can be mentioned as to determine the function’s movements.
• In order to measure the increase and decrement of a function, the chain rule is applied.
• In the field of mathematics, the positive, as well as negative values, can be acquired by considering the formulas of differentiation.  

Application of derivatives

• One of the most important usages of derivatives within real life can be found in terms of business. In order to develop different business strategies, derivatives are found to be used in the real world of business.
• In terms of biology, derivatives are used in measuring the population growth and analysis of ecosystems. 
• In terms of chemistry and economics also, derivatives play an important role by contributing to the decision-making process.   

Conclusion

In order to sum up the whole analysis, some relevant points need to be found and mentioned. There is an important formula that is integrally connected to the computation of the derivatives. The composition of more than two or two functions can be considered relevant in this regard. In terms of defining the composite functions, chain rules within the differentiation process need to be regarded as important. The importance of these identified rules can be mentioned in the usage of this in solving different problems. The minimum and maximum values of any particular function can be determined properly by utilising these identified formulas.