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 #