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

1 Answer
Mar 29, 2018

=>y' = ln(x) + 1

Explanation:

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:

  • g(x) = x
  • h(x) = ln(x)

We compute the derivatives:

  • g'(x) = 1
  • h'(x) = 1/x

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