What are the first and second derivatives of f(x)=x^8*ln(x)f(x)=x8ln(x)?

1 Answer
Dec 24, 2015

Let's remember product rule: be y=f(x)g(x)y=f(x)g(x), then y'=f'(x)g(x)+f(x)g'(x)

Explanation:

Solving:

(df(x))/(dx)=8x^7lnx+x^8(1/x)=8x^7lnx+x^7=x^7(8lnx+1)

Using product rule again:

(df(x))^2/(d^2x)=7x^6(8lnx+1)+x^7(8/x)

(df(x))^2/(d^2x)=56x^6lnx+7x^6+8x^6=56x^6lnx+15x^6

(df(x))^2/(d^2x)=x^6(56lnx+15)