Study Tips: Differentiation of an Infinite Series

This tip on calculus was contributed by one of our top tutors, Shashwat.

What you will learn from this tip:
The trick to differentiate an infinite series.


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Consider the following question:
A function y is defined as

Find at x = 0.

Solution:
The trick we use is that we multiply and divide the right hand side by (x-1). Thus,


Now we can use the division rule that we know for differentiation.

Therefore,

At x=0,

Thus, we get the answer as

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