What are the first and second derivatives of f(x)=-3x^5lnx ?

1 Answer
Dec 24, 2015

Here, we'll need the product rule, which states that for y=f(x)g(x), y'=f'(x)g(x)+f(x)g'(x)

Explanation:

Solving:

(df(x))/(dx)=(-15x^4)(lnx)+(-3x^5)(1/x)=-15x^4lnx-3x^4=color(green)(-3x^4(5lnx+1))

Second derivative follows the same logic:

(df(x))^2/(dx)=(-12x^3)(5lnx+1)+(-3x^4)(5/x)=-60x^3lnx-12-15x^3

(df(x))^2/(dx)=color(blue)(-15x^3(4lnx+1)-12)