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Question -

Differentiate in three ways mentioned below

(i) By using product rule.

(ii) By expanding the product toobtain a single polynomial.

(iii By logarithmicdifferentiation.

Do they all give the same answer?



Answer -

(i)

(ii)

(iii) 

Taking logarithm on both thesides, we obtain

Differentiating both sides withrespect to x, we obtain

From the above three observations, it can be concludedthat all the results of are same.

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