Question #0caf0

1 Answer
Oct 2, 2016

d/dx xln(1/x)=ln(1/x)-1

Explanation:

Using the product rule

d/dx f(x)g(x) = f(x)g'(x) + g(x)f'(x)

along with the derivatives

  • d/dx x = 1
  • d/dx ln(x) = 1/x

we have

d/dx xln(1/x) = d/dx xln(x^(-1))

=d/dx (-xln(x))

=-x(1/x) + (-1)ln(x)

=-1 + ln(x^(-1))

=ln(1/x)-1