Compute the indicated derivative of each of the following functions.

Question

f(x) = x^2*ln(x/3); evaluate f'(x)

Answer 1

f(x) = x^2*ln(x/3)

Find the derivative using the product rule.

d/dx(uv) =uv' +vu'

f'(x) = (d/dx)(x^2*ln(x/3))

        =(x^2)(ln(x/3))' + (ln(x/3))(x^2)'

       =(x^2)(1/(x/3))+2x(ln(x/3))

        =3x++2x(ln(x/3))