What is the derivative of $f(x)=x*ln(x)$ ?

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Answer 1 · 2014-07-23T18:39:36

The function $f(x) = x* ln(x)$ is of the form $f(x) = g(x) * h(x)$ which makes it suitable for appliance of the product rule.

Product rule says that to find the derivative of a function that's a product of two or more functions use the following formula:

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

In our case, we can use the following values for each function:

$g(x) = x$

$h(x) = ln(x)$

$g'(x) = 1$

$h'(x) = 1/x$

When we substitute each of these into the product rule, we get the final answer:

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

Learn more about the product rule here.

What is the derivative of f(x)=x*ln(x)f(x)=x*ln(x) ?