How do you differentiate $f(x)=xlnx$ using the product rule?

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Answer 1 · 2016-02-08T12:42:28

$f'(x) = ln x + 1$

For $f(x) = g(x) * h(x)$ , the product rule states that

$f'(x) = g'(x) * h(x) + g(x) * h'(x)$

In your case, let $g(x) = x$ and $h(x) = ln x$ .

Let's compute the derivatives of $g(x)$ and $h(x)$ :

$g(x) = x " " => " " g'(x) = 1$

$h(x) = ln x " " => " " h'(x) = 1/x$

Thus, you can compute the derivative as follows:

$f'(x) = g'(x) * h(x) + g(x) * h'(x)$

$= 1 * ln x + x * 1/x$

$= ln x + 1$

How do you differentiate f(x)=xlnx f(x)=xlnx using the product rule?