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

##### 1 Answer

Feb 8, 2016

#### Explanation:

For

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

In your case, let

Let's compute the derivatives of

#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 #