# How do you find the derivative of the function: f(x) = x^3 - 3x^2 - 1 evaluated at x=3?

Dec 21, 2016

$f ' \left(3\right) = 9$

#### Explanation:

differentiate each term of f(x) using the $\textcolor{b l u e}{\text{power rule}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(a {x}^{n}\right) = n a {x}^{n - 1}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow f ' \left(x\right) = 3 {x}^{2} - 6 x$

$\Rightarrow f ' \left(3\right) = 3 {\left(3\right)}^{2} - 6 \left(3\right) = 27 - 18 = 9$