Differentiate in three ways mentioned below

(i) By using product rule.

(ii) By expanding the product to obtain a single polynomial.

(iii By logarithmic differentiation.

Do they all give the same answer?

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Solution

(i)

(ii)

(iii)

Taking logarithm on both the sides, we obtain

Differentiating both sides with respect to x, we obtain

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

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Similar questions

Differentiate $(x^{2} - 5 x + 8) (x^{3} + 7 x + 9)$ in three ways mentioned below.

(a) By using product rule.

(b) By expanding the product to obtain a single polynomial.

Do they all given the same answer?

(x^{2} - 5 x + 8) (x^{3} + 7 x + 9)

\begin{matrix} Differentiate (x^{2} - 5 x + 8) (x^{3} + 7 x + 9) in ways mentioned below: (i) by using product rule \end{matrix}

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