Chain Rule Formula with Problem Solution & Solved Example

Chain rule formula is popular to compute the derivative of the composition for two or more functions. For instance, if a and b are two functions then derivative of their composition can be expressed with the help of chain rule.The mathematical representation of chain rule formula is given below –

\[\LARGE \frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}\]

This is possible to distinguish the composite functions with the chain rule. So, what is the meaning of composite functions exactly? This is a popular function whose variable is some another function. At the first glance, working with the chain rule seems daunting but don’t panic because it will be getting simpler once you start practicing it.

If you have one composite function and asked to take the derivative of the function then take the derivative as a whole, don’t consider the small functions initially. Once derivative is taken for the whole function then multiple it with the derivative of small functions. Thankfully, it is much easier to understand in action when you practice the concept continuously.

There is one important condition to follow the chain rule though. If any of the given function is not differentiable with respect to x then the chain rule is not applicable. Solve two three problems together and you will get to know where to apply the rule with a single look only. Few of the composite functions are easy to understand while few needs more practice and patient. All the best for a wonderful experience with chain rule formula learning.


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