Solution assignment 09 Product and Quotient rule

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Assignment 9

Differentiate:

$y=\ln^2(x)$

Solution

We cannot differentiate this function directly using the product rule. However, we know:

$y=\ln(x)\cdot\ln(x)$

and now we can apply the product rule:

$y'=\displaystyle\frac{1}{x}\ln(x)+\ln(x)\cdot\displaystyle\frac{1}{x}=\displaystyle\frac{2}{x}\ln(x)$

We could also have applied the Chain rule with the same result.

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