How do you use the product rule to find the derivative of #y=x*ln(x)# ?

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Answer 1 · 2018-03-29T03:34:06

#=>y' = ln(x) + 1#

#y = x * ln(x)#

The product rule states that for a function #f(x) = g(x)h(x)#, the derivative is:

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

In our equation, we have:

We compute the derivatives:

We use the product rule:

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

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

#=>f'(x) = ln(x) + 1#