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

1 Answer
Jul 23, 2014

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.